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Academic literature on the topic 'Gaussian interpolation function'

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Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Gaussian interpolation function"

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Sydorenko, Yuliia V., and Mykola V. Horodetskyi. "Modification of the Algorithm for Selecting a Variable Parameter of the Gaussian Interpolation Function." Control Systems and Computers, no. 6 (290) (December 2020): 21–28. http://dx.doi.org/10.15407/csc.2020.06.021.

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The paper presents an algorithm for selecting the optimal value of the variable parameter α of the Gaussian interpolation function to obtain the smallest possible error when interpolating the tabular data. The results of the algorithm are checked on a sample of elementary mathematical functions. For comparison, the interpolation data of the Lagrange polynomial are given. The paper presents the results of Gaussian interpolation at different α, conclusions are made about the need to applying the algorithm for selecting of its optimal value.
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Sydorenko, I., and M. Horodetskyi. "ANALYSIS OF GAUSSIAN INTERPOLATION FUNCTION ALGORITHM ON ELEMENTARY ALGEBRAIC FUNCTIONS." Modern problems of modeling 19 (September 8, 2020): 134–45. http://dx.doi.org/10.33842/2313-125x/2020/19/134/145.

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Dutra e Silva Júnior, Élvio Carlos, Leandro Soares Indrusiak, Weiler Alves Finamore, and Manfred Glesner. "A Programmable Look-Up Table-Based Interpolator with Nonuniform Sampling Scheme." International Journal of Reconfigurable Computing 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/647805.

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Interpolation is a useful technique for storage of complex functions on limited memory space: some few sampling values are stored on a memory bank, and the function values in between are calculated by interpolation. This paper presents a programmable Look-Up Table-based interpolator, which uses a reconfigurable nonuniform sampling scheme: the sampled points are not uniformly spaced. Their distribution can also be reconfigured to minimize the approximation error on specific portions of the interpolated function’s domain. Switching from one set of configuration parameters to another set, selected on the fly from a variety of precomputed parameters, and using different sampling schemes allow for the interpolation of a plethora of functions, achieving memory saving and minimum approximation error. As a study case, the proposed interpolator was used as the core of a programmable noise generator—output signals drawn from different Probability Density Functions were produced for testing FPGA implementations of chaotic encryption algorithms. As a result of the proposed method, the interpolation of a specific transformation function on a Gaussian noise generator reduced the memory usage to 2.71% when compared to the traditional uniform sampling scheme method, while keeping the approximation error below a threshold equal to 0.000030518.
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Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 02 (June 1996): 481–99. http://dx.doi.org/10.1017/s0001867800048588.

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We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance function, d(t – s) = E[(X(t) – X(s))2], and the interpolation errors in mean square and uniform metrics is studied. The method of investigation can also be applied to the analysis of different methods of interpolation. It is based on some limit results for large deviations of a sequence of Gaussian non-stationary processes and related point processes. Non-stationarity in our case means mainly the local stationary condition for the sequence of correlation functions rn(t, s), n = 1, 2, ···, which has to hold uniformly in n. Finally, we discuss some examples and an application to the calculation of the distribution function of the maximum of a continuous Gaussian process with a given precision.
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Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 2 (June 1996): 481–99. http://dx.doi.org/10.2307/1428068.

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We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance function, d(t – s) = E[(X(t) – X(s))2], and the interpolation errors in mean square and uniform metrics is studied. The method of investigation can also be applied to the analysis of different methods of interpolation. It is based on some limit results for large deviations of a sequence of Gaussian non-stationary processes and related point processes. Non-stationarity in our case means mainly the local stationary condition for the sequence of correlation functions rn(t,s), n = 1, 2, ···, which has to hold uniformly in n. Finally, we discuss some examples and an application to the calculation of the distribution function of the maximum of a continuous Gaussian process with a given precision.
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Hartman, Eric, and James D. Keeler. "Predicting the Future: Advantages of Semilocal Units." Neural Computation 3, no. 4 (December 1991): 566–78. http://dx.doi.org/10.1162/neco.1991.3.4.566.

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In investigating gaussian radial basis function (RBF) networks for their ability to model nonlinear time series, we have found that while RBF networks are much faster than standard sigmoid unit backpropagation for low-dimensional problems, their advantages diminish in high-dimensional input spaces. This is particularly troublesome if the input space contains irrelevant variables. We suggest that this limitation is due to the localized nature of RBFs. To gain the advantages of the highly nonlocal sigmoids and the speed advantages of RBFs, we propose a particular class of semilocal activation functions that is a natural interpolation between these two families. We present evidence that networks using these gaussian bar units avoid the slow learning problem of sigmoid unit networks, and, very importantly, are more accurate than RBF networks in the presence of irrelevant inputs. On the Mackey-Glass and Coupled Lattice Map problems, the speedup over sigmoid networks is so dramatic that the difference in training time between RBF and gaussian bar networks is minor. Gaussian bar architectures that superpose composed gaussians (gaussians-of-gaussians) to approximate the unknown function have the best performance. We postulate that an interesing behavior displayed by gaussian bar functions under gradient descent dynamics, which we call automatic connection pruning, is an important factor in the success of this representation.
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Khalili, Mohammad Amin, and Behzad Voosoghi. "Gaussian Radial Basis Function interpolation in vertical deformation analysis." Geodesy and Geodynamics 12, no. 3 (May 2021): 218–28. http://dx.doi.org/10.1016/j.geog.2021.02.004.

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Shen, Qiang, and Longzhi Yang. "Generalisation of Scale and Move Transformation-Based Fuzzy Interpolation." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 3 (May 20, 2011): 288–98. http://dx.doi.org/10.20965/jaciii.2011.p0288.

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Fuzzy interpolative reasoning has been extensively studied due to its ability to enhance the robustness of fuzzy systems and reduce system complexity. In particular, the scale and move transformation-based approach is able to handle interpolation with multiple antecedent rules involving triangular, complex polygon, Gaussian and bell-shaped fuzzy membership functions [1]. Also, this approach has been extended to deal with interpolation and extrapolation with multiple multi-antecedent rules [2]. However, the generalised extrapolation approach based on multiple rules may not degenerate back to the basic crisp extrapolation based on two rules. Besides, the approximate function of the extended approach may not be continuous. This paper therefore proposes a new approach to generalising the basic fuzzy interpolation technique of [1] in an effort to eliminate these limitations. Examples are given throughout the paper for illustration and comparative purposes. The result shows that the proposed approach avoids the identified problems, providing more reasonable interpolation and extrapolation.
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Lee, Lung-fei. "INTERPOLATION, QUADRATURE, AND STOCHASTIC INTEGRATION." Econometric Theory 17, no. 5 (September 25, 2001): 933–61. http://dx.doi.org/10.1017/s0266466601175043.

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This paper considers features in numerical and stochastic integration approaches for the evaluation of analytically intractable integrals. It provides a unification of these two approaches. Some important features in quadrature formulations, namely, interpolation and region partition, can provide a valuable device for the design of a stochastic simulator. An interpolating function can be used as a valuable control variate for variance reduction in simulation. We illustrate possible variance reduction by some numerical cases with Gaussian quadrature. The resulting simulator may also be regarded as a monitor of the approximation error of a quadrature.
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Platte, Rodrigo B., and Tobin A. Driscoll. "Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation." SIAM Journal on Numerical Analysis 43, no. 2 (January 2005): 750–66. http://dx.doi.org/10.1137/040610143.

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Dissertations / Theses on the topic "Gaussian interpolation function"

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Городецький, Микола Вадимович. "Вплив коефіцієнта згладжування на вигляд інтерполяційної функції Гауса." Bachelor's thesis, КПІ ім. Ігоря Сікорського, 2020. https://ela.kpi.ua/handle/123456789/36376.

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Робота присвячена аналізу впливу коефіцієнта згладжування на вигляд інтерполяційної функції Гауса. В першому розділі наведено методи розв’язання задач обробки масивів даних методами інтерполяції, в другому розділі описується теоретичні засоби класичних методів інтерполяції та інтерполяційної функції Гауса, в третьому розділі описується аналіз порівняльних результатів та проведено аналіз похибки із застосуванням варіативного коефіцієнта згладжування, в четвертому розділі описується вибір засобів програмної реалізації, в п’ятому розділі описується архітектура та методика роботи користувача з програмним продуктом.
The aim of the work is analysis of the influence of the smoothing coefficient on the form of the Gaussian interpolation function. The first section deals with methods of solving problems of data array processing by interpolation methods are given, the second section deals with the theoretical means of classical methods of interpolation and Gaussian interpolation function, the third section describes the analysis of comparative results is described and the error analysis is performed using a variable smoothing coefficient, the fourth section describes the choice of software implementation, the fifth describes the architecture of software.
Работа посвящена анализу влияния коэффициента сглаживания на вид интерполяционной функции Гаусса. В первом разделе приведены методы решения задач обработки массивов данных методами интерполяции, во втором разделе описывается теоретические основы классических методов интерполяции и интерполяционной функции Гаусса, в третьем разделе описывается анализ сравнительных результатов и проведен анализ погрешности с применением вариативного коэффициента сглаживания, в четвертом разделе описывается выбор средств программной реализации, в пятом разделе описывается архитектура и методика работы пользователя с программным продуктом.
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Larsson-Cohn, Lars. "Gaussian structures and orthogonal polynomials." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2002. http://publications.uu.se/theses/91-506-1535-1/.

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Ji, Wei. "Spatial Partitioning and Functional Shape Matched Deformation Algorithm for Interactive Haptic Modeling." Ohio University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1226364059.

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Bah, Ebrima M. "Numerické metody pro rekonstrukci chybějící obrazové informace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401582.

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The Diploma thesis deals with reconstruction of Missing data of an Image. It is done by the use of appropriate Mathematical theory and numerical algorithm to reconstruct missing information. The result of this implementation is the reconstruction of missing image information. The thesis also compares different numerical methods, and see which one of them perform best in terms of efficiency and accuracy of the given problem, hence it is used for the reconstruction of missing data.
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Book chapters on the topic "Gaussian interpolation function"

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Turgut, Umut Orcun, and Didem Gokcay. "Shape Preservation Based on Gaussian Radial Basis Function Interpolation on Human Corpus Callosum." In Spectral and Shape Analysis in Medical Imaging, 118–32. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-51237-2_10.

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"Towards a Gausslet analysis: Gaussian representations of functions." In Function Spaces, Interpolation Theory and Related Topics, edited by Michael Cwikel, Miroslav Englis, Alois Kufner, Lars-Erik Persson, and Gunnar Sparr. Berlin, New York: Walter de Gruyter, 2002. http://dx.doi.org/10.1515/9783110198058.425.

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"On Gaussian-summing identity maps between Lorentz sequence spaces." In Function Spaces, Interpolation Theory and Related Topics, edited by Michael Cwikel, Miroslav Englis, Alois Kufner, Lars-Erik Persson, and Gunnar Sparr. Berlin, New York: Walter de Gruyter, 2002. http://dx.doi.org/10.1515/9783110198058.383.

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Conference papers on the topic "Gaussian interpolation function"

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Yamaguchi, Takuro, Masaaki Ikehara, and Yasuhiro Nakajima. "Image interpolation based on weighting function of Gaussian." In 2015 49th Asilomar Conference on Signals, Systems and Computers. IEEE, 2015. http://dx.doi.org/10.1109/acssc.2015.7421329.

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Planas, Robert, Nicholas Oune, and Ramin Bostanabad. "Extrapolation With Gaussian Random Processes and Evolutionary Programming." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22381.

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Abstract Emulation plays an indispensable role in engineering design. However, the majority of emulation methods are formulated for interpolation purposes and their performance significantly deteriorates in extrapolation. In this paper, we develop a method for extrapolation by integrating Gaussian processes (GPs) and evolutionary programming (EP). Our underlying assumption is that there is a set of free-form parametric bases that can model the data source reasonably well. Consequently, if we can find these bases via some training data over a region, we can do predictions outside of that region. To systematically and efficiently find these bases, we start by learning a GP without any parametric mean function. Then, a rich dataset is generated by this GP and subsequently used in EP to find some parametric bases. Afterwards, we retrain the GP while using the bases found by EP. This retraining essentially allows to validate and/or correct the discovered bases via maximum likelihood estimation. By iterating between GP and EP we robustly and efficiently find the underlying bases that can be used for extrapolation. We validate our approach with a host of analytical problems in the absence or presence of noise. We also study an engineering example on finding the constitutive law of a composite microstructure.
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Davis, Sean, Oishik Sen, Gustaaf Jacobs, and H. S. Udaykumar. "Coupling of Micro-Scale and Macro-Scale Eulerian-Lagrangian Models for the Computation of Shocked Particle-Laden Flows." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62521.

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The accuracy and efficiency of several algorithms that couple output from full resolution micro-scale Direct Numerical Simulation computations to input for macro-scale Eulerian-Lagrangian (EL) methods for the computation of high-speed, particle-laden flow are assessed. A Stochastic Collocation method, a Gaussian Radial Basis Function (RBF) Artificial Neural Network (ANN), and an improved RBF-ANN are compared for the fitting of an analytical drag coefficient formula that depends on Mach number and Reynolds number. The improved RBF-ANN uses a clustering algorithm to enhance conditioning of interpolation matrices. The fitted drag coefficient mantle, used to trace point particles in macro-scale computations, is in excellent agreement with the analytical drag formula. The SC method requires fewer micro-scale realizations to obtain comparable accuracy of the drag coefficient. The Gaussian RBF does not converge monotonically, while the improved RBF-ANN converges algebraically and has the potential to provide error estimates.
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Luo, Huageng, Liping Wang, Don Beeson, and Gene Wiggs. "Pseudo-ARMA Model for Meta-Modeling Extrapolation." In ASME Turbo Expo 2007: Power for Land, Sea, and Air. ASMEDC, 2007. http://dx.doi.org/10.1115/gt2007-27208.

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In spite of exponential growth in computing power, the enormous computational cost of complex and large-scale engineering design problems make it impractical to rely exclusively on original high fidelity simulation codes. Therefore, there has been an increasing interest in the use of fast executing meta-models to alleviate the computational cost required by slow and expensive simulation models — especially for optimization and probabilistic design. However, many state-of-the-art meta-modeling techniques, such as Radial Basis Function (RBF), Gaussian Process (GP), and Kriging can only make good predictions in the case of interpolation. Their ability for extrapolation is not impressive since the models are mathematically constructed for interpolations. Although Multivariate Adaptive Regression Splines (MARS) and Artificial Neural Network (ANN) have been tried for extrapolation problems (forecasting), the results do not always meet accuracy requirements. The autoregressive moving-average (ARMA) model is a popular time series modeling and forecasting tool. It has been widely used in many engineering applications in which all the inputs and outputs are time dependent. Many researchers have tried to extend the time series ARMA modeling technique into so-called spatial ARMA modeling or time-space ARMA modeling. However, the time-space ARMA modeling requires extensive computation in grid data generation as well as in model building, particularly for high dimensional problems. In this paper, a pseudo-ARMA approach is proposed to strengthen meta-modeling extrapolation capability. Each input is randomly sampled at a given mean value and distribution range to form a pseudo-time series. The output variables are evaluated based on input variables, which formulate output variable pseudo time series. The pseudo-ARMA model is built based on the pseudo input and output time series. Using the constructed pseudo-ARMA model, and new input variables generated with extended distribution parameters, such as distribution means and distribution ranges, the output variables can be evaluated to achieve extrapolations. Several numerical examples are presented to demonstrate the proposed approach. The results are compared with Radial Basis Function (RBF) meta-modeling results for both interpolation and extrapolation.
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McCartney, Michael, Matthias Haeringer, and Wolfgang Polifke. "Comparison of Machine Learning Algorithms in the Interpolation and Extrapolation of Flame Describing Functions." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-91319.

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Abstract This paper examines and compares commonly used Machine Learning algorithms in their performance in interpolation and extrapolation of FDFs, based on experimental and simulation data. Algorithm performance is evaluated by interpolating and extrapolating FDFs and then the impact of errors on the limit cycle amplitudes are evaluated using the xFDF framework. The best algorithms in interpolation and extrapolation were found to be the widely used cubic spline interpolation, as well as the Gaussian Processes regressor. The data itself was found to be an important factor in defining the predictive performance of a model, therefore a method of optimally selecting data points at test time using Gaussian Processes was demonstrated. The aim of this is to allow a minimal amount of data points to be collected while still providing enough information to model the FDF accurately. The extrapolation performance was shown to decay very quickly with distance from the domain and so emphasis should be put on selecting measurement points in order to expand the covered domain. Gaussian Processes also give an indication of confidence on its predictions and is used to carry out uncertainty quantification, in order to understand model sensitivities. This was demonstrated through application to the xFDF framework.
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Strömberg, Niclas. "Reliability Based Design Optimization by Using a SLP Approach and Radial Basis Function Networks." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59522.

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In this paper reliability based design optimization by using radial basis function networks (RBFN) as surrogate models is presented. The RBFN are treated as regression models. By taking the center points equal to the sampling points an interpolation is obtained. The bias of the network is taken to be known a priori or posteriori. In the latter case, the well-known orthogonality constraint between the weights of the RBFN and the polynomial basis functions of the bias is adopted. The optimization is performed by using a first order reliability method (FORM)-based sequential linear programming (SLP) approach, where the Taylor expansions are generated in intermediate variables defined by the iso-probabilistic transformation. In addition, the reliability constraints are expanded at the most probable points which are found by using Newton’s method. The Newton algorithm is derived by proposing an in-exact Jacobian. In such manner, a FORM-based LP-formulation in the standard normal space of problems with non-Gaussian variables is suggested. The solution from the LP-problem is mapped back to the physical space and the suggested procedure continues in a sequence until convergence is reached. This is implemented for five different distributions: normal, lognormal, Gumbel, gamma and Weibull. It is also presented how the FORM-based SLP approach can be corrected by using second order reliability methods (SORM) and Monte Carlo simulations. In particular, the SORM approach of Hohenbichler is studied. The outlined methodology is both efficient and robust. This is demonstrated by solving established benchmarks as well as finite element problems.
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Hunt, Terence D., and Steven C. Gustafson. "Digital image interpolation using adaptive Gaussian basis functions." In Electronic Imaging 2004, edited by Charles A. Bouman and Eric L. Miller. SPIE, 2004. http://dx.doi.org/10.1117/12.555598.

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Qian, Hao, and Yang Chen. "A New Method of Fuzzy Interpolative Reasoning Based on Gaussian-Type Membership Function." In 2009 Fourth International Conference on Innovative Computing, Information and Control (ICICIC 2009). IEEE, 2009. http://dx.doi.org/10.1109/icicic.2009.34.

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Karri, Satyaprakash, John Charonko, and Pavlos Vlachos. "Robust Gradient Estimation Schemes Using Radial Basis Functions." In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/fedsm2008-55151.

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Utilization of Radial Basis Functions (RBFs) for gradient estimation is tested over various noisy flow fields. A novel mathematical formulation which minimizes the energy functional associated with the analytical surface fit for Gaussian (GA) and Generalized Multiquadratic (GMQ) RBFs is presented. Error analysis of the wall gradient estimation was performed at various resolutions, interpolation grid sizes, and noise levels in synthetically generated Poiseuille and Womersley flow fields for RBFs along with standard finite difference schemes. To test the effectiveness of the methods with DPIV (Digital Particle Image Velocimetry) data, the methods were compared using the velocities obtained by processing images generated from DNS data of an open turbulent channel. Random, bias and total error were computed in all cases. In the absence of noise all tested methods perform well, with error contained under 10% at all resolutions. In the presence of noise the RBFs perform robustly with a total error that can be contained under 10–15% even with 10% noise using various interpolation grid sizes, For turbulent flow data, although the total error is approximately 5% for finite difference schemes in the absence of noise, the error can go as high as 150% in the presence of as little as 1% noise. With DPIV processed data the error is 25–40% for TPS and MQ methods optimization of the fitting parameters that minimize the energy functional associated with the analytical surface using RBFs results in robust gradient estimators are obtained that are applicable to steady, unsteady and turbulent flow fields.
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Sarkar, S., K. Ghosh, and K. Bhaumik. "A Weighted Sum of Multi-scale Gaussians Generates New Near-ideal Interpolation Functions." In 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference. IEEE, 2005. http://dx.doi.org/10.1109/iembs.2005.1615959.

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