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Автор: Grafiati

Опубліковано: 7 липня 2024

Оновлено: 7 липня 2024

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1

ABIAN, ALEXANDER, and PAULA A. KEMP. "THE NATURAL RIGHT AND THE NATURAL LEFT INVERSES OF RECTANGULAR MATRICES." Tamkang Journal of Mathematics 21, no. 3 (December 1, 1990): 279–86. http://dx.doi.org/10.5556/j.tkjm.21.1990.4690.

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If an $m$ by $n$ with $m < n$ matrix $A$ has a right inverse then it has infinitely many right inverses. In fact, $K (AK )^{-1}$ is a right inverse of $A$ for many $n$ by $m$ matrices $K$ of rank $m$. The natural choice for $K$ is the transpose $A'$ of $A$. Thus, we call $A'(AA')^{-1}$ the natural right inverse of $A$. It can be used (not so obviously) to solve $AX = C$ yielding the solution $X = A'(AA')^{-1}C$ which minimizes the length $||X||$. Similarly, if an $n$ by $m$ with $m < n$ matrix $B$ has a left inverse, we call $(B'B)^{-1}B'$ the natural left inverse of $B$. It can be used (in an obvious way) in an attempt "to solve" $BX =C$ yielding the best approximate solution $X =(B'B)^{-1}B'C$ which minimizes the error $|| BX||$.

2

Iskandar, Fathur Rokhman, Imam Sucahyo, and Meta Yantidewi. "Penerapan Metode Invers kinematik Pada Kontrol Gerak Robot Lengan Tiga Derajat Bebas." Inovasi Fisika Indonesia 9, no. 2 (June 22, 2020): 64–71. http://dx.doi.org/10.26740/ifi.v9n2.p64-71.

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AbstrakRobot didefinisikan sebagai suatu instrumen yang terdiri dari perangkat keras dan perangkat lunak yang berfungsi untuk membantu pekerjaan manusia. Salah satu pekerjaan yang dapat dilakukan oleh robot adalah proses pemindahan barang dari satu tempat ke tempat yang lain. Sistem gerak robot lengan diadaptasi dari sistem gerak lengan manusia yang memiliki sendi atau disebut dengan joint dan link sebagai penghubung antar joint. Pergerakan robot lengan dapat ditentukan dengan menggunakan metode trial-error atau yang biasa dikenal dengan forward kinematik. Namun, metode ini dinilai lebih memakan waktu dan memori. Untuk mengatasi hal tersebut dibutuhkan metode yang merupakan kebalikan dari metode forward kinematik, yaitu metode invers kinematik. Metode invers kinematik merupakan metode pergerakan robot lengan dengan variabel yang diketahui adalah titik koordinat tujuan. Penelitian dilakukan dengan memberi masukan berupa koordinat (x, y, z) pada mikrokontroler. Data tersebut akan diproses menggunakan metode inver kinematik untuk mendapat sudut yang harus dituju oleh motor servo ( ). Sudut sebenarnya yang dituju robot akan diukur secara langsung menggunakan busur derajat ( ) sebagai pembanding. Dari penelitian yang dilakukan, didapatkan hasil persentase error rata-rata untuk servo 1 sebesar 0,14%, servo 2 sebesar 0,43%, dan servo 3 sebesar 6,47%, servo 3 pada robot lengan memiliki nilai minimal yang bisa dicapai yaitu sebesar 50o. Persentase error rata-rata untuk sumbu X sebesar 0,42%, sumbu Y sebesar 5,03%, dan sumbu Z sebesar 3,46%. Dari hasil tersebut dapat dikatakan bahwa metode invers kinematik merupakan metode yang baik sebagai metode kontrol gerak robot lengan.Kata Kunci: robot lengan. Invers kinematik, forward kinematik. AbstractRobot is determined as an instrument consisting of hardware and software that functions to help human work. One of the jobs that can be done by robots is the process of moving goods from one place to another. Robot arm motion system is adapted from the human arm motion system which has joints and links to connected the joints. The movement of the robot arm can be determined by using the trial-error method or commonly known as forward kinematics. However, this method consumes more time and memory. To overcome this, we need a method which is the opposite of the forward kinematics method, that is inverse kinematics method. Inverse kinematics method is a method of robot arm movement with the coordinates point of destination as the known variable. The study was conducted by providing input in the form of coordinates (x, y, z) on the microcontroller. The data will be processed using inverse kinematics method to get the desired angle that will be reached by the servo motor ( ). The actual angle that the robot is pointing to will be measured directly using a protractor ( ) as a comparison. From the experiments carried out, the average error percentage for servo 1 is 0.14%, servo 2 is 0.43%, and servo 3 is 6.47%, servo 3 on the robot arm has a minimum value that can be achieved that is equal to 50o. The average error percentage for the X axis is 0.42%, the Y axis is 5.03%, and the Z axis is 3.46%. From these results, it can be said that the inverse kinematics method is a good method as a controlling method of robot arm motion.Keywords: robot arm, inverse kinematics, forward kinematics.

3

Fronczek, Frank R. "The inverse Marsh error." Acta Crystallographica Section A Foundations and Advances 74, a1 (July 20, 2018): a60. http://dx.doi.org/10.1107/s0108767318099397.

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4

Dyer, Justin S., and Stephen A. Dyer. "Approximations to inverse error functions." IEEE Instrumentation & Measurement Magazine 11, no. 5 (October 2008): 32–36. http://dx.doi.org/10.1109/mim.2008.4630740.

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5

Lin, K. C., and P. Lu. "Inverse Simulation - An Error Analysis." SIMULATION 65, no. 6 (December 1995): 385–92. http://dx.doi.org/10.1177/003754979506500602.

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6

Maftuh, Muhammad Hadi. "Lengan Robot Pemindah Barang Berdasarkan Ukuran Tinggi." E-JOINT (Electronica and Electrical Journal Of Innovation Technology) 1, no. 2 (December 27, 2020): 36–41. http://dx.doi.org/10.35970/e-joint.v1i2.431.

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Abstrak- Penelitian dilakukan dengan tujuan untuk merancang dan membuat lengan robot pemindah barang berdasarkan ukuran tinggi. Dengan adanya lengan robot pemindah barang ini, maka ketika memindahkan benda dengan massa yang berat dan jarak yang jauh tidak perlu membutuhkan tenaga manusia. Karena hal ini dinilai kurang efektif mengingat keterbatasan kemampuan manusia dalam memindahkan barang berat dan keterbatasan waktu manusia dalam bekerja. Lengan robot ini didesain untuk mengambil dan memindahkan barang dari konveyor ke tempat penempatan barang. Lengan robot menggunakan sensor ultrasonik untuk mengidentifikasi barang. Input dari sensor tersebut akan diproses oleh mikrokontroler dan memberikan instruksi untuk pergerakan lengan robot tersebut. Input dari robot ini berupa koordinat awal dan koordinat akhir yang kemudian dikomputasikan dengan metode inverse kinematics dengan output berupa besar sudut yang dibutuhkan masing masing joint agar lengan robot mencapai titik koordinat tersebut. Hasil dari penelitian yang telah dilakukan, sensor ultrasonik dapat membedakan tipe barang yang ada dengan error terkecil sebesar 0,01% dan error terbesar 4,68%, serta sensor proximity dapat mendeteksi barang pada jarak ≤ 10 cm. Rata-rata error yang terjadi antara koordinat yang diinginkan dengan koordinat yang dihasilkan berdasarkan perhitungan invers kinematics adalah 0-2 cm. Pada pengujian pemindahan barang lengan robot dapat memindahkan sesuai dengan ukuran tinggi dengan tingkat keberhasilan 100 %. Berdasarkan hasil tersebut lengan robot pemindah barang dengan menggunakan metode inverse kinematics ini efektif dalam menjalankan fungsinya memindahkan barang.Kata kunci: Lengan robot, Inverse kinematics.

7

Sahoo, Abhilipsa, and Kaushika Patel. "Machine Learning-based Inverse Design Model of a Transistor." Indian Journal Of Science And Technology 17, no. 7 (February 15, 2024): 617–24. http://dx.doi.org/10.17485/ijst/v17i7.3076.

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Objectives: To develop an inverse design model for transistors, utilizing machine learning algorithms to predict key design parameters specifically, the length and width based on specified gain and bandwidth requirements. And to conduct a comprehensive comparative analysis with existing literature, evaluating the efficacy and novelty of the proposed model in the context of semiconductor engineering challenges and methodologies. Methods: The comprehensive dataset, comprising 30,000 values generated through LTspice simulations, forms the basis for training the machine learning model. Utilizing a Random Forest regressor as the base model and a multi-output regressor as the main model, the project involves extensive data analysis, model development, and iterative fine-tuning. Findings: The outcomes demonstrate the efficacy of the developed model in accurately predicting transistor dimensions. Performance metrics, including Mean Absolute Error (MAE), Mean Squared Error (MSE), and R-squared, highlight the precision of the model in fulfilling the specified objectives. Novelty: This study introduces a novel approach to semiconductor device design optimization, showcasing the potential of machine learning to streamline the inverse design process. The use of a multi-output regressor, feature engineering, and fine-tuning through log transformation contribute to the innovative nature of the developed model. Keywords: Machine Learning (ML) model, Random Forest regressor, multioutput regressor, Feature engineering, Finetuning

8

Lopes, Iug, Juliana Maria M. De Melo, and Brauliro Gonçalves Leal. "ESPACIALIZAÇÃO DA TEMPERATURA DO AR PARA A REGIÃO DO SUBMÉDIO SÃO FRANCISCO." IRRIGA 22, no. 1 (June 18, 2018): 177–93. http://dx.doi.org/10.15809/irriga.2017v22n1p177-193.

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ESPACIALIZAÇÃO DA TEMPERATURA DO AR PARA A REGIÃO DO SUBMÉDIO SÃO FRANCISCO IUG LOPES¹; JULIANA MARIA MEDRADO DE MELO² E BRAULIRO GONÇALVES LEAL³ ¹ Departamento de Engenharia Agrícola, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros, Dois Irmão, CEP: 52171-900 – Recife, PE. iuglopes@hotmail.com² Departamento de Agronomia, Universidade do Estado da Bahia, Rua Edgar Chastinet, s/n - São Geraldo, BA, 48905-680 – Juazeiro, BA. medrado.juliana@gmail.com³ Colegiado de Engenharia da Computação, Universidade Federal do Vale do São Francisco – Campus Juazeiro, Av. Antonio Carlos Magalhães, 510 Country Club, CEP: 48.902-300 – Juazeiro, BA. brauliro.leal@univasf.edu.br 1 RESUMO Dentre as variáveis meteorológicas requeridas para o cálculo do balanço hídrico destacam-se as temperaturas mínimas, médias e máximas do ar, que apresentam uma continuidade no quantitativo de distância e assim permitem de uma maneira mais simples a criação de campos contínuos utilizando métodos de interpolação espacial. O objetivo deste trabalho foi avaliar potências para o método de interpolação do Inverso da Potência da Distância (IPD) na espacialização de valores diários da temperatura no Submédio São Francisco, para os períodos de um ano, das estações do ano (inverno, primavera, verão e outono). Foram obtidos os parâmetros de potência do interpolador Inverso da Potência da Distância das temperaturas mínimas, médias e máximas a partir dos dados medidos em 14 estações meteorológicas automáticas do INMET em operação no Pólo de Desenvolvimento Petrolina-Juazeiro. Foram realizadas interpolações para as épocas: anual, inverno, primavera, verão e outono. A variação diária do erro relativo médio obtida, para a época ano, calculado utilizando os dados de temperatura mínima, média e máxima utilizando o valor da potência do interpolador foram iguais a 3,3; 3,4; e 3,4, respectivamente. Os valores de erro médio foram pequenos quando comparados com o erro instrumental. Palavras-chave: interpolação, validação cruzada, estação meteorológica LOPES, I; MELO, J. M. M.; LEAL, B. G. SPATIALIZATION OF AIR TEMPERATURE TO THE REGION OF SUBMEDIO SÃO FRANCISCO 2 ABSTRACT Among the meteorological variables required for the calculation of the water balance are the temperatures, which present a continuity in the quantitative distance and thus allow in a simpler way the creation of continuous fields using spatial interpolation methods. The objective of this work was to evaluate the power of the Inverse Distance Power (IPD) in the spatialization of daily values of temperature in the Submedia of São Francisco, for the one-year periods of the seasons (winter, spring, summer it's fall). The power parameters of the Inverse Distance Power Interpolator were obtained from the minimum, average and maximum temperatures from the data measured in 14 INMET automatic meteorological stations operating at the Petrolina-Juazeiro Development Pole. Interpolations were performed for annual, winter, spring, summer and fall seasons. The daily variation of the average relative error obtained for the year time, calculated using the data of minimum, average and maximum temperature using the value of the power of the interpolator were equal to 3.3; 3.4; and 3.4, respectively. The mean error values were small when compared to instrumental error. Keywords: interpolation, validation cross, meteorological station

9

Wang, P., H. Wang, Y. Q. Wang, X. Y. Zhang, S. L. Gong, M. Xue, C. H. Zhou, et al. "Inverse modeling of black carbon emissions over China using ensemble data assimilation." Atmospheric Chemistry and Physics Discussions 15, no. 15 (August 4, 2015): 20851–79. http://dx.doi.org/10.5194/acpd-15-20851-2015.

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Abstract. Emissions inventories of black carbon (BC), which are traditionally constructed using a "bottom-up" approach based on activity data and emissions factors, are considered to contain a large level of uncertainty. In this paper, an ensemble optimal interpolation (EnOI) data assimilation technique is used to investigate the possibility of optimally recovering the spatially resolved emissions bias of BC. An inverse modeling system for emissions is established for an atmospheric chemistry aerosol model and two key problems related to ensemble data assimilation in the top-down emissions estimation are discussed: (1) how to obtain reasonable ensembles of prior emissions; and (2) establishing a scheme to localize the background-error matrix. An experiment involving a one month simulation cycle with EnOI inversion of BC emissions is performed for January 2008. The bias of the BC emissions intensity in China at each grid point is corrected by this inverse system. The inversed emission over China in January is 240.1 Gg, and annual emission is about 2750 Gg, which is over 1.8 times of bottom-up emission inventory. The results show that, even though only monthly mean BC measurements are employed to inverse the emissions, the accuracy of the daily model simulation improves. Using top-down emissions, the average root-mean-square error of simulated daily BC is decreased by nearly 30 %. These results are valuable and promising for a better understanding of aerosol emissions and distributions, as well as aerosol forecasting.

10

Stefanski, Frederik, and Bartosz Minorowicz. "Open loop control of piezoelectric tube transducer." Archives of Mechanical Technology and Materials 38, no. 1 (June 28, 2018): 23–28. http://dx.doi.org/10.2478/amtm-2018-0004.

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Abstract This paper is focused on the open loop control of a piezoelectric tube actuator, hindered by a strong hysteresis. The actuator was distinguished with 22 % hysteresis, which hinders the positioning of piezoelectric actuator. One of the possible ways to solve this problem is application of an accurate analytical inversed model of the hysteresis in the control loop. In this paper generalized Prandtl-Ishlinskii model was used for both modeling and open loop control of the piezoelectric actuator. Achieved modeling error does not exceed max. 2.34 % of the whole range of tube deflection. Finally, the inverse hysteresis model was applied to the control line of the tube. For the same input signal (damped sine 0.2 Hz) as for the model estimation the positioning error was max. 4.6 % of the tube deflection. Additionally, for a verification reason three different complex harmonic functions were applied. For the verification functions, still a good positioning was obtained with positioning error of max.4.56 %, 6.75 %and5.6%of the tube deflection.

11

Marchi, Benjamin C., and Ellen M. Arruda. "Generalized error-minimizing, rational inverse Langevin approximations." Mathematics and Mechanics of Solids 24, no. 6 (February 16, 2018): 1630–47. http://dx.doi.org/10.1177/1081286517754131.

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The Langevin function is a non-invertible function, whose inverse commonly appears in statistical mechanics problems, particularly network models of rubber elasticity. This non-invertibility often results in the use of approximations. Owing to the prevalence of the inverse Langevin function, numerous forms of approximate have been proposed. Rational approximates are often employed because of their ability to admit asymptotic behavior in finite domains, similar to the exact inverse Langevin function. Despite the desired asymptotics of rational approximates, there is unavoidable error associated with the approximate within its domain. In this work, an error-minimizing approach for determining specific forms of rational approximates is generalized to approximates of arbitrary numerator and denominator orders. By expanding to general orders of rational approximates, the best approximate can be selected for an application based on either maximum relative error or function form considerations.

12

Lin, P. D., and K. F. Ehmann. "Inverse Error Analysis for Multi-axis Machines." Journal of Engineering for Industry 118, no. 1 (February 1, 1996): 88–94. http://dx.doi.org/10.1115/1.2803651.

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This paper discusses the problem of tolerance distribution among the links and joints of a multi-axis machine. By defining the maximum allowable tolerances for the position and orientation of the tool in the machine’s workspace, the allowable error tolerance limits of the link parameters and of the error motions of the joints are obtained. The solution of this problem, to be referred to as inverse error analysis, is of fundamental importance during the design stages of a new machine.

13

Clarke, C. J. S. "Error estimates in the biomagnetic inverse problem." Inverse Problems 10, no. 1 (February 1, 1994): 77–86. http://dx.doi.org/10.1088/0266-5611/10/1/007.

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14

Al-Assaad, Rayan M., and Dale M. Byrne. "Error analysis in inverse scatterometry I Modeling." Journal of the Optical Society of America A 24, no. 2 (February 1, 2007): 326. http://dx.doi.org/10.1364/josaa.24.000326.

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15

Finsterle, Stefan, and Yingqi Zhang. "Error handling strategies in multiphase inverse modeling." Computers & Geosciences 37, no. 6 (June 2011): 724–30. http://dx.doi.org/10.1016/j.cageo.2010.11.009.

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16

Ho, Ken-Chung. "Inverse error-diffusion using iterated conditional modes." Displays 30, no. 4-5 (December 2009): 175–84. http://dx.doi.org/10.1016/j.displa.2009.07.001.

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17

McCaffrey, D. F., J. R. Lockwood, and C. M. Setodji. "Inverse probability weighting with error-prone covariates." Biometrika 100, no. 3 (June 24, 2013): 671–80. http://dx.doi.org/10.1093/biomet/ast022.

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18

Lai, J. Z. C., and J. Y. Yen. "Inverse error-diffusion using classified vector quantization." IEEE Transactions on Image Processing 7, no. 12 (1998): 1753–58. http://dx.doi.org/10.1109/83.730390.

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19

Salman, Mohammad Shukri, Osman Kukrer, and Aykut Hocanin. "Recursive inverse algorithm: Mean-square-error analysis." Digital Signal Processing 66 (July 2017): 10–17. http://dx.doi.org/10.1016/j.dsp.2017.04.001.

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20

DE VITO, ERNESTO, LORENZO ROSASCO, and ANDREA CAPONNETTO. "DISCRETIZATION ERROR ANALYSIS FOR TIKHONOV REGULARIZATION." Analysis and Applications 04, no. 01 (January 2006): 81–99. http://dx.doi.org/10.1142/s0219530506000711.

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We study the discretization of inverse problems defined by a Carleman operator. In particular, we develop a discretization strategy for this class of inverse problems and we give a convergence analysis. Learning from examples, as well as the discretization of integral equations, can be analyzed in our setting.

21

Muhamad Alif Haji Sismat. "Inverse Translation Quality." JALL | Journal of Arabic Linguistics and Literature 1, no. 2 (April 13, 2022): 91–105. http://dx.doi.org/10.59202/jall.v1i2.363.

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This paper aims to analyse the quality of inverse translation and to see whether or not trainee translators, such as undergraduate language students, can produce translations between foreign languages, and whether or not post-editing machine translation and translation memories, have any effect on the Malay students’ performance. Through error analysis approach, this paper also aims to reveal the contributing factors to the mistakes the students did in their translations and uncover the nature of Google Translate by identifying the recurring types of errors in the MT outputs. Results revealed that the translation technologies, particularly in the post-editing modified translation memories and machine translation tasks, helped the students improved the quality of their translations, suggesting that non-native speakers can be highly skilled professional translators with years of experience and proper training. Based on the error analysis, syntactic and lexical errors seem to be problematic in Google Translate in both Arabic-English and English-Arabic translations, implying that proper guidelines are crucial in post-editing so that post-editors can be aware of the potential recurrent errors and not overlook them. Also, the study identified that linguistic interference might have significantly influenced the students’ performance as the three languages differ from one another in many aspects.

22

Risher, D. W., L. M. Schutte, and C. F. Runge. "The Use of Inverse Dynamics Solutions in Direct Dynamics Simulations." Journal of Biomechanical Engineering 119, no. 4 (November 1, 1997): 417–22. http://dx.doi.org/10.1115/1.2798288.

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Previous attempts to use inverse dynamics solutions in direct dynamics simulations have failed to replicate the input data of the inverse dynamics problem. Measurement and derivative estimation error, different inverse dynamics and direct dynamics models, and numerical integration error have all been suggested as possible causes of inverse dynamics simulation failure. However, using a biomechanical model of the type typically used in gait analysis applications for inverse dynamics calculations of joint moments, we produce a direct dynamics simulation that exactly matches the measured movement pattern used as input to the inverse dynamic problem. This example of successful inverse dynamics simulation demonstrates that although different inverse dynamics and direct dynamics models may lead to inverse dynamics simulation failure, measurement and derivative estimation error do not. In addition, inverse dynamics simulation failure due to numerical integration errors can be avoided. Further, we demonstrate that insufficient control signal dimensionality (i.e., freedom of the control signals to take on different “shapes”), a previously unrecognized cause of inverse dynamics simulation failure, will cause inverse dynamics simulation failure even with a perfect model and perfect data, regardless of sampling frequency.

23

Shamma, J. S., and D. E. Whitney. "A Method for Inverse Robot Calibration." Journal of Dynamic Systems, Measurement, and Control 109, no. 1 (March 1, 1987): 36–43. http://dx.doi.org/10.1115/1.3143817.

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A method is described for the inverse calibration of a manipulator or robot. Inverse calibration is defined to be finding the joint angles necessary to drive a robot to a desired endpoint location. The joint angles recommended by the robot controller’s internal model will not, in general, drive the robot to the desired location because of inaccuracies in this model. Inverse calibration seeks to reduce the error. Unlike previous work in calibration, the method reported here does not require modeling any specific phenomena that may cause the error; hence it is not limited in accuracy by inability to identify all the error sources. The method consists of finding approximation functions by which corrections are made to the encoder readings recommended by the robot’s internal model. These functions are found by measuring the error at discrete locations throughout a region of the robot’s workspace and then least-squares fitting third order trivariate polynomials to the error samples. A forward calibration (one which reports actual tool location from given encoder readings) based on the above method is also described. The inverse calibration is tested on a six DOF PUMA simulation. Results show that the endpoint location error can be reduced from an average of about 1.2 mm down to an average of about 0.12 mm.

24

Fausan, Fausan, Gandung Sugita, and Sukayasa Sukayasa. "PROFIL KESALAHAN SISWA DALAM MENYELESAIKAN SOAL MATRIKS BERDASARKAN JENIS KELAMIN DI SMA NEGERI 7 PALU." Aksioma 8, no. 2 (September 24, 2019): 110–24. http://dx.doi.org/10.22487/aksioma.v8i2.208.

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Abstrak: Penelitian ini merupakan penelitian kualitatif yang bertujuan untuk memperoleh profil kesalahan yang dilakukan siswa dalam menyelesaikan soal matriks berdasarkan jenis kelamin di SMA Negeri 7 Palu. Data dikumpulkan dengan cara metode tes dan wawancara. Subjek penelitian terdiri dari satu siswa laki-laki (SH) dan satu siswa perempuan (DS). Hasil Penelitian menunjukkan bahwa kesalahan konseptual yang dilakukan siswa laki-laki (SH) yaitu : 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan tidak menerapkan rumus invers, 4) kesalahan konsep invers matriks dan 5) kesalahan konsep adjoin. Kesalahan prosedural yang dilakukan siswa laki-laki berupa 1) kesalahan dalam melakukan perhitungan, 2) kesalahan tidak menyederhanakan dan 3) kesalahan tidak menuliskan tanda operasi pada matriks. Sedangkan kesalahan konseptual yang dilakukan siswa perempuan (DS) yaitu: 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan konsep adjoin dan 4) kesalahan konsep invers matriks. Kesalahan prosedural yang dilakukan siswa perempuan berupa 1) kesalahan dalam melakukan perhitungan. Siswa laki-laki banyak melakukan kesalahan dari pada siswa perempuan dikarenakan, siswa laki-laki tidak teliti dan terburu-buru dalam menyelesaikan soal matriks. Sedangkan siswa perempuan tidak terlalu banyak melakukan kesalahan dikarenakan cenderung lebih teliti dan cermat dalam menyelesaikan soal matriks. Kata kunci: Profil Kesalahan, Jenis Kelamin dan Matriks Abstract: This research is a qualitative research which aims to obtain a profile of errors students make in solving matrix problems based on sex in SMA 7 Palu. Data was collected by means of test and interview methods. The research subjects consisted of one male student (SH) and one female student (DS). The results showed that the conceptual errors made by male students (SH) were: 1) errors not understanding the concept of matrix multiplication formula, 2) errors in matrix multiplication concepts, 3) errors not applying inverse formulas, 4) inverse matrix concept errors and 5 ) the error of the adjoin concept. Procedural errors made by male students in the form of 1) errors in making calculations, 2) errors do not simplify and 3) errors do not write the operation mark on the matrix. Whereas the conceptual errors made by female students (DS) are: 1) errors do not understand the concept of matrix multiplication formula, 2) errors in the concept of matrix multiplication, 3) errors in adjoining concepts and 4) inverse matrix concept errors. Procedural errors made by female students in the form of 1) errors in carrying out calculations. Male students make a lot of mistakes than female students because , male students are not careful and in a hurry to solve the matrix problem. Whereas female students don't make too many mistakes becausethey tend to be more thorough and careful in solving matrix problems. Keywords: Error Profile, Gender and Matrix

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Damayanti CR, Mey, and Teti Sofia Yanti. "Regresi Poisson Invers Gaussian (PIG) untuk Pemodelan Jumlah Kasus Pneumonia pada Balita di Provinsi Jawa Tengah Tahun 2019." Jurnal Riset Statistika 1, no. 2 (February 13, 2022): 143–51. http://dx.doi.org/10.29313/jrs.v1i2.523.

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Abstract. Poisson regression is a non-linear regression model used on non-negative count or discrete data. Poisson regression is included in the Generalized Linear Model (GLM). In Poisson regression there is an assumption that must be met, that is equidispersion where the value of the variance in the response variable (Y) must be the same as the average value. If in Poisson regression modeling there is an overdispersion or underdispersion and it is ignored, the test will be less accurate because the standard error value will be underestimated. Poisson Inverse Gaussian Regression Model (PIG) can overcome overdispersion data. The Poisson Inverse Gaussian (PIG) distribution is a mixed Poisson distribution. PIG regression is used to model the count data which has a high slope and skews to the right. Maximum likelihood method was used to estimate the parameters in the PIG regression model. Pneumonia is an acute infection that causes inflammation of the lung tissue. The case of pneumonia in children under five is one form of discrete data. The results of the PIG regression model were compared based on the Akaike Information Criterion (AIC) to obtain the best model. From the results of hypothesis testing, it was concluded that the percentage of children under five who had received measles immunization and the percentage of children under five who had received DPT immunization had a significant effect on the of pneumonia cases in children under five. By using the AIC value, the Poisson Inverse Gaussian (PIG) regression model is obtained, that is: . Abstrak. Regresi poisson merupakan model regresi non-linear yang digunakan pada data cacah atau diskrit non-negatif. Regresi Poisson termasuk kedalam Generalized Linear Model (GLM). Pada regresi Poisson terdapat asumsi yang harus dipenuhi yaitu equidispersi dimana nilai variansi pada variabel respon (Y) harus sama dengan nilai rata-ratanya. Apabila dalam pemodelan regresi Poisson terjadi kasus overdispersi atau underdispersi dan hal tersebut diabaikan maka pengujian akan menjadi kurang akurat karena nilai standard error akan menjadi underestimate. Model Regresi Poisson Invers Gaussian (PIG) dapat mengatasi data overdispersi. Distribusi Poisson Invers Gaussian (PIG) merupakan mixed poisson distribution. Regresi PIG digunakan untuk memodelkan data cacah yang memiliki kemiringan yang tinggi dan menceng ke kanan. Metode maximum likelihood digunakan untuk menaksir parameter pada model regresi PIG.. Pneumonia merupakan infeksi akut yang menyebabkan peradangan pada jaringan paru-paru. Kasus pneumonia pada balita merupakan salah satu bentuk dari data diskrit. Hasil model regresi PIG dibandingkan berdasarkan Akaike Information Criterion (AIC) untuk memperoleh model terbaik. Dari hasil pengujian hipotesis diperoleh kesimpulan bahwa persentase balita yang pernah mendapatkan imunisasi campak dan persentase balita yang pernah mendapatkan imunisasi DPT berpengaruh signifikan terhadap jumlah kasus pneumonia pada balita. Dengan memperhatikan nilai AIC didapatkan model regresi Poisson Invers Gaussian (PIG) yaitu: .

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Ratajczak, Joanna. "Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse." Archives of Control Sciences 25, no. 1 (March 1, 2015): 35–50. http://dx.doi.org/10.1515/acsc-2015-0003.

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Abstract The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory.

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Li, P., W. Y. Xu, L. W. Song, and Y. Y. Qiu. "A Novel Inversion Method of Manufacturing Flaws in the Packaging of Conformal Load-Bearing Antenna Structure." International Journal of Antennas and Propagation 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/795323.

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Composite material is widely used in the conformal load-bearing antenna structure (CLAS), and the manufacturing flaws in the packaging process of the CLAS will lead to the degradation of its wave-transparent property. For this problem, a novel inverse method of the flaw’s dimension by antenna-radome system’s far field data has been proposed. Two steps are included in the inversion: the first one is the inversion from the far filed data to the transmission coefficient of the CLAS’s radome; the second one is the inversion from the transmission coefficient to the flaw’s dimension. The inversion also has a good potential for the separable multilayer composite material radome. A 12.5 GHz CLAS with microstrip antenna array is used in the simulation, which indicates the effectiveness of the novel inversion method. Finally, the error analysis of the inversion method is presented by numerical simulation; the results is that the inversed error could be less than 10%, if the measurement error of far field data is less than 0.45 dB in amplitude and ±5° in phase.

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Amerault, Clark, and Xiaolei Zou. "Comparison of Model-Produced and Observed Microwave Radiances and Estimation of Background Error Covariances for Hydrometeor Variables within Hurricanes." Monthly Weather Review 134, no. 3 (March 1, 2006): 745–58. http://dx.doi.org/10.1175/mwr3073.1.

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Abstract A radiative transfer model was updated to better simulate Special Sensor Microwave Imager (SSM/I)–observed brightness temperatures in areas of high ice concentration. The difference between the lowest observed and model-produced brightness temperatures at 85 GHz has been reduced from over 100 K to roughly 20 K. Probability distribution functions of model-produced and SSM/I-observed brightness temperatures show that the model overestimates the areas of precipitation, but overall matches the SSM/I observations quite well. Estimates of vertical background error covariance matrices and their inverses were calculated for all hydrometeor variables (both liquid and frozen). For cloud and rainwater, the largest values in the matrices are located in the lower levels of the atmosphere, while the largest values in the cloud ice, snow, and graupel matrices are in the upper levels of the atmosphere. The inverse background matrices can be used as weightings for hydrometeor variables in assimilation experiments involving rain-affected observations.

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BEILINA, LARISA, and CLAES JOHNSON. "A POSTERIORI ERROR ESTIMATION IN COMPUTATIONAL INVERSE SCATTERING." Mathematical Models and Methods in Applied Sciences 15, no. 01 (January 2005): 23–35. http://dx.doi.org/10.1142/s0218202505003885.

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We prove an a posteriori error estimate for an inverse acoustic scattering problem, where the objective is to reconstruct an unknown wave speed coefficient inside a body from measured wave reflection data in time on parts of the surface of the body. The inverse problem is formulated as a problem of finding a zero of a Jacobian of a Lagrangian. The a posterori error estimate couples residuals of the computed solution to weights the reconstruction reflecting the sensitivity of the reconstruction obtained by solving an associated linaerized problem for the Hessian of the Lagrangian. We show concrete examples of reconstrution including a posteriori error estimation.

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Henrion, Didier, Jean B. Lasserre, and Martin Mevissen. "Mean Squared Error Minimization for Inverse Moment Problems." Applied Mathematics & Optimization 70, no. 1 (January 23, 2014): 83–110. http://dx.doi.org/10.1007/s00245-013-9235-z.

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31

Keller-McNulty, S., and W. J. Kennedy. "Error-free computation of a reflesive generalized inverse." Linear Algebra and its Applications 67 (June 1985): 157–67. http://dx.doi.org/10.1016/0024-3795(85)90193-4.

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Ping Wah Wong. "Inverse halftoning and kernel estimation for error diffusion." IEEE Transactions on Image Processing 4, no. 4 (April 1995): 486–98. http://dx.doi.org/10.1109/83.370677.

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Djebbouri, M., D. Djebouri, and R. Naoum. "Wavelet-based inverse halftoning for error diffused halftones." AEU - International Journal of Electronics and Communications 59, no. 2 (May 2005): 128–33. http://dx.doi.org/10.1016/j.aeue.2004.11.039.

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Marchi, Benjamin C., and Ellen M. Arruda. "An error-minimizing approach to inverse Langevin approximations." Rheologica Acta 54, no. 11-12 (October 16, 2015): 887–902. http://dx.doi.org/10.1007/s00397-015-0880-9.

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Echevarria, Miguel G., Tomas Kasemets, Jean-Philippe Lansberg, Cristian Pisano, and Andrea Signori. "Matching factorization theorems with an inverse-error weighting." Physics Letters B 781 (June 2018): 161–68. http://dx.doi.org/10.1016/j.physletb.2018.03.075.

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36

Kincanon, Eric. "Error propagation in the Abel hill inverse problem." International Journal of Applied Mathematical Research 12, no. 1 (July 5, 2023): 1–2. http://dx.doi.org/10.14419/ijamr.v12i1.32295.

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Abel’s Hill considers the problem of how to determine the shape of the hill from information on the return time of a rolled ball. Though this problem has been solved for piecewise monotonic functions, the issue of error propagation has not been addressed. This paper considers how errors in time measurement correlate to errors in determining the shape of the hill.

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Myrontsov, Mykyta, Oleksiy Karpenko, and Volodymyr Horbulin. "Quantitative method for determining the solution error of the inverse problem in the electrometry of oil and gas wells." E3S Web of Conferences 280 (2021): 09003. http://dx.doi.org/10.1051/e3sconf/202128009003.

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Determining the quantitative degree of connection between logging error and the corresponding error of oil and gas wells electrometry inverse problem solving is considered. A quantitative method to determine the magnitude of the error of solving the inverse problem depending on the magnitude of the logging error for a given model of a single layer or section as a whole is described. Examples of determining the error of the inverse problem for real well materials, taking into account the actual measurement error, are given. A method for determining the characteristics of the spatial resolution of electrometry methods is described. Examples of its use for low-frequency induction logging equipment are given. The proposed methods allow to determine the areas of equivalent solutions and the areas of existence of stable / unstable solutions of the inverse electrometry problem.

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Zontini, Diego D., Maikon L. Mirkoski, and João A. F. Santos. "Error bounds in the computation of outer inverses with generalized Schultz iterative methods and its use in computing of Moore-Penrose inverse." Applied Mathematics and Computation 440 (March 2023): 127664. http://dx.doi.org/10.1016/j.amc.2022.127664.

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Leonov, Alexander S. "Source recovery with a posteriori error estimates in linear partial differential equations." Journal of Inverse and Ill-posed Problems 28, no. 5 (November 1, 2020): 677–92. http://dx.doi.org/10.1515/jiip-2020-0055.

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AbstractWe consider inverse problems of recovering a source term in initial boundary value problems for linear multidimensional partial differential equations (PDEs) of a general form. A universal stable method suitable for solving such inverse problems is proposed. The method allows one to obtain in the same way approximations to exact sources in different kinds of PDEs using various types of linear supplementary conditions specified with an error. The method is suitable for both spacewise dependent and time-dependent sources. The method consists in preliminary calculation of a special matrix introduced in the article, the matrix of the source inverse problem, and then inverting it using Tikhonov regularization. The matrix can be obtained by solving a number of initial boundary value problems in question with sources in the form of basis functions. Having spent some time for preliminary finding the matrix (for example, by finite element method with a sufficiently detailed grid), we can then use this matrix to quickly solve the inverse problem with various data. The same technique can be applied to solve inverse source problems in linear steady-state PDEs. We also propose an a posteriori error estimation method for the obtained approximate solution and give a numerical algorithm for such estimation. In addition, a relationship is established between the posterior estimate and the lower estimate for the optimal accuracy of solving the inverse problem. The proposed method of solving inverse source problems is illustrated by the numerical solution of model examples for one-dimensional and two-dimensional PDEs of different kinds with a posteriori error estimates.

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Bannikova, T. M., V. M. Nemtsov, N. A. Baranova, G. N. Konygin, and O. M. Nemtsova. "A method for estimating the statistical error of the solution in the inverse spectroscopy problem." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 58 (November 2021): 3–17. http://dx.doi.org/10.35634/2226-3594-2021-58-01.

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A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.

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Abou-Elyazied Abdallh, Ahmed, and Luc Dupré. "Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 3 (April 29, 2014): 856–67. http://dx.doi.org/10.1108/compel-10-2012-0230.

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Purpose – Magnetic material properties of an electromagnetic device (EMD) can be recovered by solving a coupled experimental numerical inverse problem. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the EMD need to be perfectly modeled using a complex numerical model. However, these fine models demand a high computational time. Alternatively, less accurate coarse models can be used with a demerit of the high expected recovery errors. The purpose of this paper is to present an efficient methodology to reduce the effect of stochastic modeling errors in the inverse problem solution. Design/methodology/approach – The recovery error in the electromagnetic inverse problem solution is reduced using the Bayesian approximation error approach coupled with an adaptive Kriging-based model. The accuracy of the forward model is assessed and adapted a priori using the cross-validation technique. Findings – The adaptive Kriging-based model seems to be an efficient technique for modeling EMDs used in inverse problems. Moreover, using the proposed methodology, the recovery error in the electromagnetic inverse problem solution is largely reduced in a relatively small computational time and memory storage. Originality/value – The proposed methodology is capable of not only improving the accuracy of the inverse problem solution, but also reducing the computational time as well as the memory storage. Furthermore, to the best of the authors knowledge, it is the first time to combine the adaptive Kriging-based model with the Bayesian approximation error approach for the stochastic modeling error reduction.

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Kwac, Lee Ku, and Hong Gun Kim. "Nano Positioning Control for Ultra-Precision Machining Using Inverse Hysteresis Model." Advanced Materials Research 123-125 (August 2010): 735–38. http://dx.doi.org/10.4028/www.scientific.net/amr.123-125.735.

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In this study, inverse-hysteresis model, which can inversely calculate input voltage for desired displacement, is suggested for tracking performance. In this paper, tracking performance and movement precision of piezoelectric actuator as operating parts of ultra-precision cutting unit is improved using feedback control of inverse-hysteresis model to remove hysteresis property. PID feedback control is studied as controller to compensate the error in inverse-hysteresis model. In addition, straightness error of spindle, thermal expansion error of mechanical structure is analyzed to detect movement error property in ultra-precision machining. Via machining performance evaluation using ultra-precision machining experiments, the machining precision of ultra-precision CNC lathe can be improved.

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Yang, Liangdong, Jinxin Liu, Qian Zhang, Ruqiang Yan, and Xuefeng Chen. "Spline adaptive inverse control scheme with filtered error feedback." Nonlinear Dynamics 106, no. 3 (October 18, 2021): 2309–28. http://dx.doi.org/10.1007/s11071-021-06882-6.

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44

Alifanov, O. M., and A. V. Nenarokomov. "Boundary inverse heat conduction problem: algorithm and error analysis." Inverse Problems in Engineering 9, no. 6 (June 2001): 619–44. http://dx.doi.org/10.1080/174159701088027784.

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Stein, Gillian Z., and June M. Juritz. "Linear models with an inverse gaussian poisson error distribution." Communications in Statistics - Theory and Methods 17, no. 2 (January 1988): 557–71. http://dx.doi.org/10.1080/03610928808829640.

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46

Jódar, L., E. Ponsoda, and G. Rodríguez. "Approximations and error bounds for computing the inverse mapping." Applications of Mathematics 42, no. 2 (April 1997): 99–110. http://dx.doi.org/10.1023/a:1022291010828.

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Conti, A., M. Z. Win, and M. Chiani. "On the inverse symbol-error probability for diversity reception." IEEE Transactions on Communications 51, no. 5 (May 2003): 753–56. http://dx.doi.org/10.1109/tcomm.2003.811433.

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Connor, Brian J., Hartmut Boesch, Geoffrey Toon, Bhaswar Sen, Charles Miller, and David Crisp. "Orbiting Carbon Observatory: Inverse method and prospective error analysis." Journal of Geophysical Research: Atmospheres 113, no. D5 (March 6, 2008): n/a. http://dx.doi.org/10.1029/2006jd008336.

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Ganachaud, Alexandre. "Error Budget of Inverse Box Models: The North Atlantic." Journal of Atmospheric and Oceanic Technology 20, no. 11 (November 2003): 1641–55. http://dx.doi.org/10.1175/1520-0426(2003)020<1641:eboibm>2.0.co;2.

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Vedder, John D. "Simple approximations for the error function and its inverse." American Journal of Physics 55, no. 8 (August 1987): 762–63. http://dx.doi.org/10.1119/1.15018.

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