Статті в журналах: "Precision Calculation"

1

RODRIGUES, B. O., L. A. C. P. DA MOTA, and L. G. S. DUARTE. "NUMERICAL CALCULATION WITH ARBITRARY PRECISION." International Journal of Modern Physics E 16, no. 09 (October 2007): 3045–48. http://dx.doi.org/10.1142/s0218301307009014.

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The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and rounding errors may induce the user to incorrect interpretation of his or her answer. In this work, we have developed a computational package to minimize this kind of error by offering arbitrary precision numbers and calculation. This is very important in Physics where we can work with numbers too small and too big simultaneously.

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2

Fukuchi, Tsugio. "A whole high-accuracy numerical calculation system for the 1D Poisson equation by the interpolation finite difference method." AIP Advances 12, no. 10 (October 1, 2022): 105315. http://dx.doi.org/10.1063/5.0093636.

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The interpolation finite difference method (IFDM) allows free numerical analysis of elliptic partial differential equations over arbitrary domains. Conventionally, in the finite difference method (FDM), the calculation is performed using the second-order accuracy central difference. For engineering problems, second-order accuracy calculations are often sufficient. On the other hand, much research has been carried out to improve the accuracy of numerical calculations. Although there is much research in the FDM field, the development of numerical calculations by the spectral method is decisive in improving the calculation accuracy. Numerical calculations are usually performed by double precision calculations. If double precision calculations ensure 15 significant digits in floating point computing, such numerical calculations will be the ultimate goal to reach. A numerical calculation that does not seem to have an error even though it originally has an error is defined as a virtual error-zero (VE0) calculation. In this paper, we will examine an overall picture of high-accuracy numerical calculation by the IFDM in the numerical calculation of the 1D Poisson equation. It becomes clear that a VE0 calculation is always possible in the numerical calculation method, defined as the compact interpolation finite difference scheme [( m)].

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3

Ricke, Darrell O., and Steven Schwartz. "Fast P(RMNE): Fast forensic DNA probability of random man not excluded calculation." F1000Research 6 (December 20, 2017): 2154. http://dx.doi.org/10.12688/f1000research.13349.1.

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High throughput sequencing (HTS) of DNA forensic samples is expanding from the sizing of short tandem repeats (STRs) to massively parallel sequencing (MPS). HTS panels are expanding from the FBI 20 core Combined DNA Index System (CODIS) loci to include SNPs. The calculation of random man not excluded, P(RMNE), is used in DNA mixture analysis to estimate the probability that a person is present in a DNA mixture. This calculation encounters calculation artifacts with expansion to larger panel sizes. Increasing the floating-point precision of the calculations allows for increased panel sizes but with a corresponding increase in computation time. The Taylor series higher precision libraries used fail on some input data sets leading to algorithm unreliability. Herein, a new formula is introduced for calculating P(RMNE) that scales to larger SNP panel sizes while being computationally efficient (patent pending).

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Ricke, Darrell O., and Steven Schwartz. "Fast P(RMNE): Fast forensic DNA probability of random man not excluded calculation." F1000Research 6 (October 31, 2018): 2154. http://dx.doi.org/10.12688/f1000research.13349.2.

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High throughput sequencing (HTS) of DNA forensic samples is expanding from the sizing of short tandem repeats (STRs) to massively parallel sequencing (MPS). HTS panels are expanding from the FBI 20 core Combined DNA Index System (CODIS) loci to include SNPs. The calculation of random man not excluded, P(RMNE), is used in DNA mixture analysis to estimate the probability that a person is present in a DNA mixture. This calculation encounters calculation artifacts with expansion to larger panel sizes. Increasing the floating-point precision of the calculations allows for increased panel sizes but with a corresponding increase in computation time. The Taylor series higher precision libraries used fail on some input data sets leading to algorithm unreliability. Herein, a new formula is introduced for calculating P(RMNE) that scales to larger SNP panel sizes while being computationally efficient (patent pending).

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5

Zhang, Yi Tong, Zhan Qi Hu, and Hong Li Zhang. "A Calculating Method of the Least Feeding Times in Cylinder Cam’s Grinding." Key Engineering Materials 359-360 (November 2007): 181–84. http://dx.doi.org/10.4028/www.scientific.net/kem.359-360.181.

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The accurate calculation and the approximate calculations of the cylinder cam’s curve enveloping surface in single-tool-position-compensation are compared. It is proved that the approximate formula is enough precision for engineering purpose. Based on the analyses for the approximate formula, the calculating method of the least feeding times of the multi-tool-position-compensation is proposed. This method provides theoretical foundation for complex surface’s high efficiency and great precision grinding as well as optimal machining control.

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6

Orr, T. LL, and C. Cherubini. "Use of the ranking distance as an index for assessing the accuracy and precision of equations for the bearing capacity of piles and at-rest earth pressure coefficient." Canadian Geotechnical Journal 40, no. 6 (December 1, 2003): 1200–1207. http://dx.doi.org/10.1139/t03-063.

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In many geotechnical design situations, a number of different calculation models have been developed to predict the value of a particular quantity required for use in design calculations, for example, the bearing capacities of driven and root piles, and K0, the at-rest earth pressure coefficient. In this paper the authors show how the dependability of different calculation methods can be compared and assessed using a synthetic probabilistic approach and the ranking distance (RD) index. Measured values, Qmeas, are compared with calculated values, Qcalc, using the "bias factor," defined as the ratio Qmeas/Qcalc. The bias factor values obtained using a particular calculation method are processed to evaluate the "accuracy" and "precision" by calculating a central tendency and a variability statistical parameter, respectively, from the values. The RD index is a comprehensive statistical parameter for assessing the dependability of a particular calculation method and is based on the central tendency and variability. Using the ratios between calculated and measured bearing capacity and earth pressures values, the RD index is used to assess the accuracy and precision of the most frequently used pile driving formulae, two equations for the bearing capacity of root piles, and seven equations for the at-rest earth pressure coefficient.Key words: accuracy, precision, probabilistic approach, ranking distance.

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7

Zhong, Liang, Guang Xiang Xu, and Feng Zeng. "Analysis and Comparison on Typical Methods for Predicting Composite Roughness of River." Advanced Materials Research 518-523 (May 2012): 4111–14. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.4111.

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Composite roughness is an important parameter in river hydraulic calculations. In this paper, various typical methods for predicting composite roughness of river were summarized, including Einstein Method, Lotter Method, JIANG Method and Weighted Average Method, their theoretical rigors were discussed from both perspectives of minimum energy dissipation principle and analytical analysis, and their calculation precisions were verified by a large number of flume test data. Research shows that Einstein Method complies with the principle of minimum energy dissipation, also is the necessary and sufficient condition of resistance equation having unique solution, and its calculation precision is higher, therefore, Einstein Method is more suitable for composite resistance calculation of river with single cross section.

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8

Jijie Zhu. "Calculation of geometric dilution of precision." IEEE Transactions on Aerospace and Electronic Systems 28, no. 3 (July 1992): 893–95. http://dx.doi.org/10.1109/7.256323.

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9

Ścibisz-Mordelska, Katarzyna. "Lower Precision calculation for option pricing." Computer Science 18, no. 4 (2017): 431. http://dx.doi.org/10.7494/csci.2017.18.4.2361.

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10

Zabolitzky, J. G., D. J. Bergman, and D. Stauffer. "Precision calculation of elasticity for percolation." Journal of Statistical Physics 44, no. 1-2 (July 1986): 211–23. http://dx.doi.org/10.1007/bf01010913.

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11

Song, Xu Dong, Jian Wei Mu, Rui Fang Feng, and Zhan Zhi Qiu. "Variable Precision Rough Set Optimization Algorithm for Constructing Decision Tree." Advanced Materials Research 181-182 (January 2011): 43–48. http://dx.doi.org/10.4028/www.scientific.net/amr.181-182.43.

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The calculation of Variable precision explicit region is an improved algorithm for constructing decision tree on the use of variable precision rough set model. For defects in the process of calculating the explicit region—in the process of calculating the explicit region, the more the number of attributes is, the greater the value of specific areas is, it puts forward the calculation algorithm that the number of attributes limits specific area. This algorithm enhances the accuracy of the calculation process. It can effectively reduce the trend that the more the classification of attributes is, the greater the greater the value of specific areas is. In the meanwhile, it also effectively improves the accuracy of the algorithm. By introducing the support and confidence, it simplifies the resulted tree, and improves the generalization ability of the tree. Finally, the validity of the method is verified through experimental analysis.

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12

Long, Chen, Xia Xintao, Zheng Haotian, and Qiu Ming. "Friction Torque Behavior as a Function of Actual Contact Angle in Four-point-contact Ball Bearing." Applied Mathematics and Nonlinear Sciences 1, no. 1 (January 1, 2016): 53–64. http://dx.doi.org/10.21042/amns.2016.1.00005.

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AbstractThe friction is a key factor of rolling bearing performance, especially for those precision transmission fields. All the top rolling bearing manufactures provide their calculating models on friction torque. However, there is great difference between the calculation result and measured value. Two calculation methods on friction torque of four-point-contact ball bearing, considered different factors involving the calculation, are compared and researched for discovering the key influence factor. A specific test is development to verify the theoretical analysis and a precision control method on friction torque with lower cost in production is proposed.

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13

WITTIG, ALEXANDER, and MARTIN BERZ. "COMPUTATION OF HIGH-ORDER MAPS TO MULTIPLE MACHINE PRECISION." International Journal of Modern Physics A 24, no. 05 (February 20, 2009): 1019–39. http://dx.doi.org/10.1142/s0217751x09044474.

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The Beam Dynamics simulation package in COSY INFINITY is built upon a differential algebra data type. With it, it is possible to compute transfer maps or arbitrary systems to arbitrary order. However, this data type is limited by the precision of the underlying floating point number model provided by the computer processor. We will present a method to extend the effective precision of the calculations based purely on standard floating point operations. Those algorithms are then integrated into the differential algebra data type to efficiently extend the available precision, without unnecessarily affecting overall efficiency. To that effect, the precision of each coefficient is adjusted automatically during the calculation. We will then proceed to show the effectiveness of our implementation by calculating high precision maps of combinations of homogeneous dipole segments, for which the exact results are known, and comparing the high precision coefficients with the results produced by the traditional COSY beam physics package.

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14

Fenton, Tanis R., Thibault Senterre, and Ian J. Griffin. "Time interval for preterm infant weight gain velocity calculation precision." Archives of Disease in Childhood - Fetal and Neonatal Edition 104, no. 2 (July 11, 2018): F218—F219. http://dx.doi.org/10.1136/archdischild-2018-314843.

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Calculation of weight gain velocity is used to guide nutrition and fluid management practices in neonatal intensive care units. Calculations over short time periods may be more responsive to management changes, but less precise. Weight gain velocity calculated over 5 to 7+ days have lower variability and less noise than shorter periods.

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15

Wei, Hong Hu, and Yan Bao. "Precision of Earthwork Computation by Grid." Advanced Materials Research 243-249 (May 2011): 5864–68. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.5864.

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Based on theoretical models,the accuracy is analyzed to earthwork calculation in grid method under different terrain rolling rates, different grid widths.And the basic relationship between relative error of theoretical calculation and grid and terrain parameters is obtained, which can be used for evaluation of practical earthwork calculation.

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16

Rymarczyk, Tomasz, and Jan Sikora. "ON PRECISION ACOUSTIC WAVE CALCULATION IN A FREQUENCY DOMAIN." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 12, no. 2 (June 30, 2022): 64–68. http://dx.doi.org/10.35784/iapgos.2966.

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The accuracy of the calculation of acoustic problems formulated in the frequency domain is presented in this work. The issues of the acoustic point sources modelling were discussed and the influence of frequency as well as the impact of the geometry of the analysed area on the accuracy of calculations were indicated. Speaking about the influence of geometry, we mean not only discretization but also the configuration of the considered area, such as for example point sources localization close to the outer edge.

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17

Wang, Hao Peng, Xiao Jing Li, and Jing Zhang. "Study on Inversion Surface Parameters of Remote-Sensing Information Serving Vegetation-Surface." Applied Mechanics and Materials 635-637 (September 2014): 914–17. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.914.

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The paper studied on the inversion surface parameters of remote-sensing information serving for vegetation surface. First, presented the inversion of surface temperature based on four parts: calculation of brightness temperatureyntax of L-systems, calculation of atmospheric transmissivity, calculation of surface emissivity, and D. Precision evaluation on inversion result. Secondly, calculating the atmospheric transmissivity .

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18

Lichman, G. I., S. A. Belykh, and A. N. Marchenko. "METHODS OF APPLYING FERTILIZERS IN PRECISION AGRICULTURE." Agricultural Machinery and Technologies 12, no. 4 (September 27, 2018): 4–9. http://dx.doi.org/10.22314/2073-7599-2018-12-4-4-9.

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It is impossible to achieve the planned yields, product quality, and economic efficiency in agricultural production using only organic fertilizers. joint application of organic and solid mineral fertilizers solves the problem of replenishing the soil content of nitrogen, phosphorus and other elements used by plants. The authors have carried out the research of new methods of variable-rate application of mineral fertilizers in plant growing, allowing to increase the profitability of agricultural production. (Research purpose) is to develop new methods of variable-rate application of mineral fertilizers in crop production, which will allow increasing the profitability of crop production as compared with the conventional methods of applying fertilizers basing on average field indicators. (Materials and methods) The authors have developed a calculation technique implemented in the VBA Excel computer program for determining the main indicators: gross output, fertilizer saving, profit, etc. The main variable to change in the calculations is the planned yield based on average field parameters. At the end of the calculation process, the values of the best result for gross harvest output and profit are displayed on the screen. The research objects for the calculation were represented by elementary areas of crop areas of three farms – “Prodresurs”, Agropoligon VIUA, and “Murminskoye” with different soil types: chernozem, loamy, and sandy-loam. (Results and discussion) The method of proportional variable-rate application of fertilizers on three types of soils gives a stable increase in profit as compared with the application of fertilizers basing on the average field indicators. (Conclusions) Calculations have shown that under the specified conditions and at the equal yield of 30 c/ha the application of organomineral fertilizers is the most effective, profitability has accounted for 40 percents – on mesopodzol sandy-loam soils; 8.7 percents – on sod-podzolic soils; and 1.3 percents – on black soils. The method of proportional variable-rate application of mineral fertilizers accompanied with variable-rate application of organic fertilizers makes it possible to reduce the amount of mineral fertilizers applied by half.

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19

Qian, MA, and FENG Xin. "Calculation precision of pollutant load of rivers." Journal of Lake Sciences 24, no. 5 (2012): 663–66. http://dx.doi.org/10.18307/2012.0503.

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20

Chen, Chien-Sheng, Yi-Jen Chiu, Chin-Tan Lee, and Jium-Ming Lin. "Calculation of Weighted Geometric Dilution of Precision." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/953048.

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To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP), instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS) devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN) and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error.

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21

Akita, Kensuke, and Masahide Yamaguchi. "A precision calculation of relic neutrino decoupling." Journal of Cosmology and Astroparticle Physics 2020, no. 08 (August 5, 2020): 012. http://dx.doi.org/10.1088/1475-7516/2020/08/012.

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22

Csorgo, Sandor, and Gordon Simons. "Precision Calculation of Distributions for Trimmed Sums." Annals of Applied Probability 5, no. 3 (August 1995): 854–73. http://dx.doi.org/10.1214/aoap/1177004708.

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23

Wang, Shengquan, Chao Wang, Yong Cai, and Guangyao Li. "A novel parallel finite element procedure for nonlinear dynamic problems using GPU and mixed-precision algorithm." Engineering Computations 37, no. 6 (February 22, 2020): 2193–211. http://dx.doi.org/10.1108/ec-07-2019-0328.

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Purpose The purpose of this paper is to improve the computational speed of solving nonlinear dynamics by using parallel methods and mixed-precision algorithm on graphic processing units (GPUs). The computational efficiency of traditional central processing units (CPUs)-based computer aided engineering software has been difficult to satisfy the needs of scientific research and practical engineering, especially for nonlinear dynamic problems. Besides, when calculations are performed on GPUs, double-precision operations are slower than single-precision operations. So this paper implemented mixed precision for nonlinear dynamic problem simulation using Belytschko-Tsay (BT) shell element on GPU. Design/methodology/approach To minimize data transfer between heterogeneous architectures, the parallel computation of the fully explicit finite element (FE) calculation is realized using a vectorized thread-level parallelism algorithm. An asynchronous data transmission strategy and a novel dependency relationship link-based method, for efficiently solving parallel explicit shell element equations, are used to improve the GPU utilization ratio. Finally, this paper implements mixed precision for nonlinear dynamic problems simulation using the BT shell element on a GPU and compare it to the CPU-based serially executed program and a GPU-based double-precision parallel computing program. Findings For a car body model containing approximately 5.3 million degrees of freedom, the computational speed is improved 25 times over CPU sequential computation, and approximately 10% over double-precision parallel computing method. The accuracy error of the mixed-precision computation is small and can satisfy the requirements of practical engineering problems. Originality/value This paper realized a novel FE parallel computing procedure for nonlinear dynamic problems using mixed-precision algorithm on CPU-GPU platform. Compared with the CPU serial program, the program implemented in this article obtains a 25 times acceleration ratio when calculating the model of 883,168 elements, which greatly improves the calculation speed for solving nonlinear dynamic problems.

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24

Sun, Hui, Fanchang Meng, Zhihou Zhang, Cheng Gao, and Mingchen Liu. "High-precision Joint 2D Traveltime Calculation for Seismic Processing." Earth Sciences Research Journal 22, no. 4 (October 1, 2018): 327–34. http://dx.doi.org/10.15446/esrj.v22n4.77362.

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Fast Marching Method (FMM) boasts high calculation efficiency and strong adaptability and stability while being applied to seismic traveltime. However, when it is applied to the largescale model, the calculation precision of FMM is insufficient. FMM has poor calculation precision near the source, which is an essential reason for the low accuracy of the whole algorithm. This paper puts forward a joint traveltime calculation method to address the problem. Wavefront Construction (WFC) with a relatively high calculation accuracy rather than FMM is adopted for calculation of the grid nodes’ traveltime near the source. After that, FMM is used to calculate the seismic traveltime in the remaining area. Joint traveltime calculation method greatly improves the calculation accuracy of the source’s surrounding area and the calculation accuracy of FMM. According to the new method, FMM is still adopted for the calculation of most grid nodes in the model, so the high calculation efficiency of FMM is maintained. Multiple numerical models are utilized to verify the above conclusions in the paper.

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25

Yuan, Guo Ming, Jian Wang, Hong Xiao, and Ming Lei Li. "Research on Online Model of Vertical Rolling Force in Hot Strip Roughing Trains." Advanced Materials Research 145 (October 2010): 198–203. http://dx.doi.org/10.4028/www.scientific.net/amr.145.198.

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For low prediction precision of online model for vertical rolling force in roughing trains of hot strip mill, the process of hot strip roughing trains was simulated by the FEM simulation software DEFORM. The cause of low prediction precision of rolling force during vertical rolling was analyzed. Then the new method for calculating deformation degree when edge rolling was presented by analysis of the FEM simulated results. The formula of external stress status modulus, which is fit for the vertical rolling force calculation, was obtained by analytic regression. Furthermore, a new formula about rolling force calculation was gained. It was approved that the prediction precision was obviously enhanced compared with the practical data for vertical rolling force.

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Nakano, Masuo, Hisashi Yashiro, Chihiro Kodama, and Hirofumi Tomita. "Single Precision in the Dynamical Core of a Nonhydrostatic Global Atmospheric Model: Evaluation Using a Baroclinic Wave Test Case." Monthly Weather Review 146, no. 2 (January 30, 2018): 409–16. http://dx.doi.org/10.1175/mwr-d-17-0257.1.

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Abstract Reducing the computational cost of weather and climate simulations would lower electric energy consumption. From the standpoint of reducing costs, the use of reduced precision arithmetic has become an active area of research. Here the impact of using single-precision arithmetic on simulation accuracy is examined by conducting Jablonowski and Williamson’s baroclinic wave tests using the dynamical core of a global fully compressible nonhydrostatic model. The model employs a finite-volume method discretized on an icosahedral grid system and its mesh size is set to 220, 56, 14, and 3.5 km. When double-precision arithmetic is fully replaced by single-precision arithmetic, a spurious wavenumber-5 structure becomes dominant in both hemispheres, rather than the expected baroclinic wave growth only in the Northern Hemisphere. It was found that this spurious wave growth comes from errors in the calculation of gridcell geometrics. Therefore, an additional simulation was conducted using double precision for calculations that only need to be performed for model setup, including calculation of gridcell geometrics, and single precision everywhere else, meaning that all calculations performed each time step used single precision. In this case, the model successfully simulated the growth of the baroclinic wave with only small errors and a 46% reduction in runtime. These results suggest that the use of single-precision arithmetic will allow significant reduction of computational costs in next-generation weather and climate simulations using a fully compressible nonhydrostatic global model with the finite-volume method.

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27

Sechenov, Pavel A. "Solution to the problem of thermal conductivity in a two-dimensional formulation on a graphics processing unit using parallel computing." Yugra State University Bulletin 18, no. 2 (August 7, 2022): 104–12. http://dx.doi.org/10.18822/byusu202202104-112.

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Subject: technology and algorithms of parallel programming. Objective: to compare the execution speed of a sequential algorithm on a central processor with a parallel algorithm on a graphics processor when solving a two-dimensional thermal conductivity problem. Methods: the Crank Nicholson method modified by the author for solving the problem of two-dimensional thermal conductivity on a graphics processor. Research results: 1. The solution of the two-dimensional thermal conductivity problem according to the Crank Nicholson scheme is not absolutely parallel and the maximum possible acceleration is not achieved 2. With a matrix dimension of 16 by 16 and single precision, the execution time on the GPU turned out to be 1.32 1.72 times faster than on the CPU. With a 32 by 32 matrix dimension, the execution time on the GPU turned out to be 3.66 6.07 times faster than on the CPU. 3. When calculating with double precision, the greatest acceleration is observed at 71.89 with 10 iterations of calculation, if there are more than 104 iterations, then the acceleration in calculations on a GPU with double precision approaches calculations with single precision.

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Sechenov, Pavel A. "Solution to the problem of thermal conductivity in a two-dimensional formulation on a graphics processing unit using parallel computing." Yugra State University Bulletin 18, no. 2 (August 7, 2022): 104–12. http://dx.doi.org/10.18822/byusu202202104-112.

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Subject: technology and algorithms of parallel programming. Objective: to compare the execution speed of a sequential algorithm on a central processor with a parallel algorithm on a graphics processor when solving a two-dimensional thermal conductivity problem. Methods: the Crank Nicholson method modified by the author for solving the problem of two-dimensional thermal conductivity on a graphics processor. Research results: 1. The solution of the two-dimensional thermal conductivity problem according to the Crank Nicholson scheme is not absolutely parallel and the maximum possible acceleration is not achieved 2. With a matrix dimension of 16 by 16 and single precision, the execution time on the GPU turned out to be 1.32 1.72 times faster than on the CPU. With a 32 by 32 matrix dimension, the execution time on the GPU turned out to be 3.66 6.07 times faster than on the CPU. 3. When calculating with double precision, the greatest acceleration is observed at 71.89 with 10 iterations of calculation, if there are more than 104 iterations, then the acceleration in calculations on a GPU with double precision approaches calculations with single precision.

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29

Lin, Xiaobin, Chengzhi Zhang, Meng Xie, and Nan Chen. "Research on Calculation Algorithms of Sea Target Velocity and Course for Sea Radar." MATEC Web of Conferences 175 (2018): 03044. http://dx.doi.org/10.1051/matecconf/201817503044.

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Sea Radar is an important technical measure for protecting national maritime resources and island sovereignty. The calculation of sea target velocity and course is important to monitor and track sea targets for sea radar, for calculation precision is directly related to the tracking effect of sea target. This paper systematically studies the problem on calculation of sea target velocity and course for sea radar, explicates the relevant technical principles, proposes effective algorithms for calculating sea target velocity and course based on multi-frame accumulative information, and gives a corresponding solution suitable for the scenario of sea target maneuvering. Finally, based on comparison analysis of real radar data and Automatic Identification System (AIS) data, we verify the precision of our algorithms.

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30

Cherepanska, I. Y., A. Y. Sazonov, N. I. Krushynska, V. A. Priadko, and M. V. Lukiniuk. "Quaternion Method of Calculating Angles while Measuring via Goniometric Precision Instrument System." Bulletin of the Karaganda University. "Physics" Series 101, no. 1 (March 30, 2021): 46–56. http://dx.doi.org/10.31489/2021ph1/46-56.

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The article is devoted to the topical problem: increasing accuracy and performance of angle measurements necessary in various branches of science and technology. One of the ways of increasing accuracy and performance of angle measurements is using modern algorithmic methods and mathematic devices for processing measurement information. Thus, in order to increase accuracy and speed of angle measurements on the example of the well-known goniometric precision instrument system (GPIS), it was offered quaternion calculation of angle values while performing goniometric measurements in the work. The efficiency of quaternion calculation is unquestioned as quaternions unlike other traditional methods (in particular matrix with the use of Euler angles, direction cosines) are presented only with four parameters describing angle positions of the objects and have only one connection equation unlike six equations for matrix methods, in particular for direction cosines. The suggested quaternion calculation is used in GPDS as general theoretic and information basis of contactless precision goniometric measurements in preliminary setting navigation sensitive elements (NSE), plane angles, pyramid prisms etc. The usage of the developed quaternion calculation enabled to increase accuracy by 0,25 (in 3 times) and measurement performance in 9 times (up to 6.5 sec.) in comparison with the famous ones. Applying quaternion calculation of angle values implies using a smaller RAM capacity of PC that increases performance of system work. Besides, a smaller amount of mathematic operations performed in quaternion way of calculating angles, except increasing performance, enables to decrease a rounding error in calculation results that is accumulated in multiple measurements and may reach great values. Thus, accuracy and performance of measurements increase.

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31

Zhao, Jin Fang, and Qun Zhao. "Typical Calculation Method of Stress Intensity Factors and Crack Growth Criterions on Infinite Plate Containing Hole-Edge Cracks." Advanced Materials Research 568 (September 2012): 154–58. http://dx.doi.org/10.4028/www.scientific.net/amr.568.154.

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This paper introduces a finite element analysis software FRANC2D/L to calculate the stress intensity factor (SIF) and simulate the crack growth. Samples with infinite plate containing center crack, one hole-edge crack and two symmetrical hole-edge cracks were analyzed by this software. Comparing the SIF calculation results of the three samples based on displacement correlation method, J-integral method and virtual crack closure integral method, the results show that the three methods are all suitable for calculating the SIF problems, and the calculation precision of J-integral method and virtual crack closure integral method are better. Comparing the three crack growth criterion of maximum circumferential stress, maximum strain energy release rate and minimum strain energy density, the calculation velocity and precision of maximum circumferential stress criterion and minimum strain energy density criterion are prior to maximum strain energy release rate criterion. The calculating time and angle error of maximum strain energy release rate criterion is larger than that of the other two criterions．

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32

Chen, Bing Xia, and Jian Cheng Tan. "Theoretical Line Loss Calculation in 10kV Power Distribution Network Based on an Improved Alternative Method." Applied Mechanics and Materials 241-244 (December 2012): 687–92. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.687.

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Theoretical line loss calculation is the basis of making line loss analysis and loss-reduction decision. Due to technical constraints in the past, traditional algorithms on theoretical line loss calculation used a large number of simplified calculations. This paper proposes a new online method of line loss calculation in distribution networks which is based on PQU (active power, reactive power and voltage) load curves. Based on a new kind of metrical equipment and the proposed method, the power loss calculation system has been developed and has been tested on several rural power networks. The results prove that the method improves the assumptions of traditional algorithms and calculation precision.

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33

Liu, Yu, Zhi Yu Wen, and Hong Yun Yang. "Precision Calculation for Stiffness of the Complex Microstructure." Advanced Materials Research 60-61 (January 2009): 135–40. http://dx.doi.org/10.4028/www.scientific.net/amr.60-61.135.

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The stiffness of microstructure is an important parameter of the microsensor. It is usually obtained by FEM approach, which is difficult to give an analytical expression. This paper reports on a 2-D microaccelerometer with the complex microstructure. Its main axial stiffness is carried out by using force method as well as principle of work and strain energy. During the deduction, deformation of all beams is taken into account, so the theoretical results are in accordance with that of FEM approach very well and the error is less than one in thousand. Furthermore, we neither introduce the other assumptions nor design the special dimension. So this methodology is strict in theory, and can be extended to analysis for the displacement and stiffness of the symmetric and statically indeterminate microstructure.

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34

Hu Linting, 胡林亭, 李佩军 Li Peijun, and 秦少刚 Qin Shaogang. "Calculation method of the pod laser indication precision." Infrared and Laser Engineering 45, no. 6 (2016): 0617012. http://dx.doi.org/10.3788/irla201645.0617012.

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35

HOFERICHTER, M., V. BARU, C. HANHART, B. KUBIS, A. NOGGA та D. R. PHILLIPS. "PRECISION CALCULATION OF THE π-d SCATTERING LENGTH". International Journal of Modern Physics A 26, № 03n04 (10 лютого 2011): 589–91. http://dx.doi.org/10.1142/s0217751x11052128.

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We present a calculation of the π-d scattering length in the framework of chiral perturbation theory (ChPT) with focus on virtual-photon effects. Using data on pionic deuterium and pionic hydrogen atoms, we extract the isoscalar and isovector pion–nucleon scattering lengths [Formula: see text] and [Formula: see text], as well as—via the Goldberger–Miyazawa–Oehme sum rule—the charged-pion–nucleon coupling constant [Formula: see text]

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36

Wu, Qixue. "Precision calculation of electronicgJfactors forn3S1states of4He and7Li+ion." Journal of Physics B: Atomic, Molecular and Optical Physics 39, no. 20 (October 10, 2006): 4213–19. http://dx.doi.org/10.1088/0953-4075/39/20/018.

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37

Mougeot, X. "Towards high-precision calculation of electron capture decays." Applied Radiation and Isotopes 154 (December 2019): 108884. http://dx.doi.org/10.1016/j.apradiso.2019.108884.

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38

Li, Chao, Yingming Song, Zehuan Zhang, Jie Mao, Weiwei Yuan та Bo Wang. "A Novel and High-Precision Method for Calculating the γ-Ray Build-Up Factor for Multilayer Shields". Science and Technology of Nuclear Installations 2021 (25 січня 2021): 1–15. http://dx.doi.org/10.1155/2021/8860762.

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In the field of radiation protection, the point-kernel code method is a practical tool widely used in the calculation of 3-D radiation field, and the accuracy of the point-kernel integration method strongly depends on the accuracy of the build-up factor. It is well known that calculation of the build-up factor for single-layer shields is composed of single material, but it is very complicated to calculate the build-up factor for multilayer shields (MLBUF). Recently, a novel and high-precision method based on the deep neural network (DNN) for calculating MLBUF has been proposed. In this paper, the novel method is described completely by slab models. Through the study of photon transport in multilayer shields, the parameters that mainly affect the calculation of build-up factor are analyzed. These parameters are trained by DNN as the input vectors, and the build-up factor for multilayer shields is predicted based on the trained DNN. The results predicted by DNN confirm that the method can calculate the build-up factor for multilayer shields quickly and accurately. The method has been preliminarily applicated into a 3-D radiation field calculation software, and it has proved that the method for calculating MLBUF has a broad application prospects in 3-D radiation field calculation.

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39

Zuo, Bin, Bao Yu Wang, and Le Yi Yang. "Forming Load Calculation of Hot Precision Forging of Cylindrical Gears." Applied Mechanics and Materials 456 (October 2013): 425–28. http://dx.doi.org/10.4028/www.scientific.net/amm.456.425.

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The Tooth Impact Factor was defined and introduced into the formula of forming load of closed-upsetting. Thus the formula for calculating the forming load of hot precision forging of cylindrical gears was put forward. The equation for the Tooth Impact Factor was fitted using the data from FE simulation of forging process in which gears with different modules were forged. Some forging tests for gears were conducted and the forming load was measured to ensure the validity of the formula. The tests also revealed that the formula is suitable for forming load calculation of hot precision forging of both spur and helical gears in a wide size range.

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40

Andrianova, Olga N., Evgeniya S. Teplukhina, Gennady M. Zherdev, Zhanna V. Borovskaya, and Andrey P. Zhirnov. "Precision neutronic calculations of experiments on the neutron transmission through the reflector layers at the BFS critical facilities for expanding the verification database to justify lead cooled fast reactor designs." Nuclear Energy and Technology 6, no. 4 (November 20, 2020): 269–74. http://dx.doi.org/10.3897/nucet.6.60303.

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The paper presents the results of the efforts concerned with expanding the verification database and estimating the calculation uncertainty of the power density in the steel reflector of lead cooled fast reactor designs based on experiments performed in different years at the BFS critical assemblies by analyzing and revising earlier calculation and experimental studies on the transmission of neutrons through the steel reflector layers. The discussion includes experiments at the BFS-66 critical assembly to model neutron and photon fluxes in the reactor core shielding compositions, as well as experiments at the BFS-64 and BFS-80-2 critical assemblies to model the transmission of neutrons and gamma quanta through the reflector layers of various materials. The information provided in earlier materials with the descriptions of the above experiments has been analyzed and expanded through respective data required to prepare precision calculation models for Monte-Carlo neutronic codes. Precision neutronic models have been developed based on actualized and updated data with a detailed description of the BFS heterogeneous structure and experimental devices, and test calculations have been carried out to confirm their efficiency. The calculations of key neutronic characteristics measured at the BFS-66, -64 and -80-2 assemblies were performed using codes based on the Monte Carlo method (MCU-BR, MCNP, MMK-RF, MMK-ROKOKO) with BNAB-RF and MDBBR50 neutron data and the ROSFOND evaluated neutron data library. The developed precision calculation neutronic models of the experiments discussed can be used to justify lead cooled fast reactor designs, to verify neutronic codes and neutron data, and to evaluate the associated uncertainties.

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41

Tian, Boyuan. "The Way to Detect Exoplanetary Systems and the Limitations of the Doppler Method." Theoretical and Natural Science 5, no. 1 (May 25, 2023): 178–81. http://dx.doi.org/10.54254/2753-8818/5/20230374.

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According to current astronomical developments, Doppler and lensing methods are the two most important methods used by astronomers to detect extrasolar planetary systems. Unlike the lensing method, which requires the use of high-precision astronomical telescopes to measure stellar luminosity variations, the Doppler method can rely on simple stellar redshift phenomena and calculations to accurately predict the existence of extraterrestrial planets, their masses, orbital radii, and other basic characteristics. Therefore, Doppler's method will be the most widely used method to measure planetary systems. Based on the derivation of Kepler's third law, the formulas for calculating the masses and orbital distances of planets are discussed and a python program for easy calculation is presented. Also, the limitations of Doppler's method and possible calculation errors are collected, organized, and explained.

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42

Wolever, Thomas M. S. "Effect of blood sampling schedule and method of calculating the area under the curve on validity and precision of glycaemic index values." British Journal of Nutrition 91, no. 2 (February 2004): 295–300. http://dx.doi.org/10.1079/bjn20031054.

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To evaluate the suitability for glycaemic index (GI) calculations of using blood sampling schedules and methods of calculating area under the curve (AUC) different from those recommended, the GI values of five foods were determined by recommended methods (capillary blood glucose measured seven times over 2·0 h) in forty-seven normal subjects and different calculations performed on the same data set. The AUC was calculated in four ways: incremental AUC (iAUC; recommended method), iAUC above the minimum blood glucose value (AUCmin), net AUC (netAUC) and iAUC including area only before the glycaemic response curve cuts the baseline (AUCcut). In addition, iAUC was calculated using four different sets of less than seven blood samples. GI values were derived using each AUC calculation. The mean GI values of the foods varied significantly according to the method of calculating GI. The standard deviation of GI values calculating using iAUC (20·4), was lower than six of the seven other methods, and significantly less (P<0·05) than that using netAUC (24·0). To be a valid index of food glycaemic response independent of subject characteristics, GI values in subjects should not be related to their AUC after oral glucose. However, calculating GI using AUCmin or less than seven blood samples resulted in significant (P<0·05) relationships between GI and mean AUC. It is concluded that, in subjects without diabetes, the recommended blood sampling schedule and method of AUC calculation yields more valid and/or more precise GI values than the seven other methods tested here. The only method whose results agreed reasonably well with the recommended method (ie. within ±5 %) was AUCcut.

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43

Liu, Dingjin, Bo Li, and Guofeng Liu. "Calculation of Surface Offset Gathers Based on Reverse Time Migration and Its Parallel Computation with Multi-GPUs." Applied Sciences 11, no. 22 (November 12, 2021): 10687. http://dx.doi.org/10.3390/app112210687.

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As an important method for seismic data processing, reverse time migration (RTM) has high precision but involves high-intensity calculations. The calculation an RTM surface offset (shot–receiver distance) domain gathers provides intermediary data for an iterative calculation of migration and its velocity building. How to generate such data efficiently is of great significance to the industrial application of RTM. We propose a method for the calculation of surface offset gathers (SOGs) based on attribute migration, wherein, using migration calculations performed twice, the attribute profile of the surface offsets can be obtained, thus the image results can be sorted into offset gathers. Aiming at the problem of high-intensity computations required for RTM, we put forth a multi-graphic processing unit (GPU) calculative strategy, i.e., by distributing image computational domains to different GPUs for computation and by using the method of multi-stream calculations to conceal data transmission between GPUs. Ultimately, the computing original efficiency was higher relative to a single GPU, and more GPUs were used linearly. The test with a model showed that the attributive migration methods can correctly output SOGs, while the GPU parallel computation can effectively improve the computing efficiency. Therefore, it is of practical importance for this method to be expanded and applied in industries.

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44

Liu, Jing, and Yi Jun Deng. "Research on the Recursive Method for Real Time Variance Calculation." Advanced Materials Research 433-440 (January 2012): 3196–99. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.3196.

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In the area of manufacturing and industrial engineering, variance calculation is the basic method to monitor the performance of instrument. In this paper, the recursive formula of real-time variance calculation is been put forward. Then it is possible to calculate the variance at real time without save the historical data. Experiment results shows that the new method for calculate the variance can greatly improve the calculating efficiency with high precision.

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45

Liu, Yan Xin, Han Xiang Wang, Qian Qian Fu, Xiang Xiang Yang, and Guo Dong Ding. "The Construction of the SGW-Based Bar-Beam Elements." Applied Mechanics and Materials 423-426 (September 2013): 1202–6. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.1202.

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PsdVoigt2 function was used to fit SGW function and a series of bar beam elements based on the theory of SGW and wavelet finite element were constructed. Traditional finite element polynomial interpolation was replaced by the SGW scaling function and transformation matrix was utilized to transform wavelet interpolation coefficients to physical space. Thereby the shape function and element were constructed. The precision of a series of bar beam elements constructed with the SGW scale function as the interpolation function were verified by the calculation cases. The calculation results showed that the precision of the SGW-based element constructed was higher in calculating the deformation and strain. And the SGW-based bar beam element constructed enriched the element library of wavelet-finite element method.

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46

Li, Ling Ling, Guang Pu Xu, Yong Ling Kang, and Xue Dong Ma. "Simulation Calculation of Tilting Torque for Mixed Iron Car." Advanced Materials Research 421 (December 2011): 267–70. http://dx.doi.org/10.4028/www.scientific.net/amr.421.267.

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Tilting torque of mixed iron car is an important parameter in designing tilting mechanism. In the past, calculating tilting torque of the mixed iron car mostly depended on manual calculation with low calculating speed and calculating precision. This paper adopts Solidworks software to simulate and calculate tilting torque of the 300t mixed iron car, and overcome the above drawbacks. According to the calculating, the tilting torque’s curve can be obtained, which provides a theoretical reference for determining power of tilting motor, designing tilting mechanism and judging the tilting safety.

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47

Huang, Xiong Fei, Fang Zhu, and Na Wei. "Fit Degree Calculation of an Aircraft Part Manufacturing Process." Advanced Materials Research 989-994 (July 2014): 3153–56. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.3153.

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Aircraft manufacturing process normally requires very high precision assembly parts which are achieved in practice by a high-precision machining parts followed by a high coordination degree assembly process. The current practice in aircraft parts manufacturing process is that the manufacturing cycle is long, the rework rate is high and the manufacturing precision is difficult to improve. This can be sometimes infeasible or very costly. In this paper, we consider a fit degree calculation method to achieve precision aircraft parts with economical manufacturing processes. We consider an analytical approach to establish a physical process model to guide the design and machining process of assembly parts, which can assume the fit degree. The results show that the approach can obtain the nearly optimal process parameters at designated fit degree. At last, a case is developed to verify the proposed methods.

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48

Sadkov, V. D., Yu V. Eremeev, and A. B. Ivanov. "Calculation of accurate alignment elements of precision chip-resistors." Radioelectronics and Communications Systems 53, no. 1 (January 2010): 48–51. http://dx.doi.org/10.3103/s0735272710010085.

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49

Zhang, Pei-Pei, Zhen-Xiang Zhong, Zong-Chao Yan, and Ting-Yun Shi. "Precision calculation of fine structure in helium and Li +." Chinese Physics B 24, no. 3 (February 26, 2015): 033101. http://dx.doi.org/10.1088/1674-1056/24/3/033101.

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50

Lensky, V., V. Baru, J. Haidenbauer, C. Hanhart, A. Kudryavtsev та U. G. Meißner. "Precision calculation of γd↦πnn within chiral perturbation theory". European Physical Journal A 26, № 1 (жовтень 2005): 107–23. http://dx.doi.org/10.1140/epja/i2005-10154-7.

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