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Journal articles on the topic 'Inverse method'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 June 2025

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1

K.C. Mishra, K. C. Mishra. "Inverse Homotopy Perturbation Method for Nonlinear systems." International Journal of Scientific Research 2, no. 4 (2012): 61–64. http://dx.doi.org/10.15373/22778179/apr2013/86.

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2

Prasad, K. Manjunatha, and M. David Raj. "Bordering method to compute Core-EP inverse." Special Matrices 6, no. 1 (2018): 193–200. http://dx.doi.org/10.1515/spma-2018-0016.

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Abstract Following the work of Kentaro Nomakuchi[10] and Manjunatha Prasad et.al., [7] which relate various generalized inverses of a given matrix with suitable bordering,we describe the explicit bordering required to obtain core-EP inverse, core-EP generalized inverse. The main result of the paper also leads to provide a characterization of Drazin index in terms of bordering.

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3

Soleymani, F., M. Sharifi, and S. Shateyi. "Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/731562.

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This paper presents a computational iterative method to find approximate inverses for the inverse of matrices. Analysis of convergence reveals that the method reaches ninth-order convergence. The extension of the proposed iterative method for computing Moore-Penrose inverse is furnished. Numerical results including the comparisons with different existing methods of the same type in the literature will also be presented to manifest the superiority of the new algorithm in finding approximate inverses.

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4

Wei, Wang Tian, Xue Xing Heng, and Liu Ru Xun. "Filtering inverse method." Inverse Problems 3, no. 1 (1987): 143–48. http://dx.doi.org/10.1088/0266-5611/3/1/016.

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5

Artidiello, Santiago, Alicia Cordero, Juan R. Torregrosa, and María P. Vassileva. "Generalized Inverses Estimations by Means of Iterative Methods with Memory." Mathematics 8, no. 1 (2019): 2. http://dx.doi.org/10.3390/math8010002.

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A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an approximation of the Moore–Penrose inverse and Drazin inverse are obtained. The convergence and the order of convergence is presented in each case. Some numerical tests allowed us to confirm the theoretical results and to compare the performance of our method with other known ones. With these results, the iterative methods with memory appear for the first time for estimating the solution of a nonlinear matrix equations.

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6

Bin Jebreen, Haifa, and Yurilev Chalco-Cano. "An Improved Computationally Efficient Method for Finding the Drazin Inverse." Discrete Dynamics in Nature and Society 2018 (October 17, 2018): 1–8. http://dx.doi.org/10.1155/2018/6758302.

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Drazin inverse is one of the most significant inverses in the matrix theory, where its computation is an intensive and useful task. The objective of this work is to propose a computationally effective iterative scheme for finding the Drazin inverse. The convergence is investigated analytically by applying a suitable initial matrix. The theoretical discussions are upheld by several experiments showing the stability and convergence of the proposed method.

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7

Oldenburg, D. W., and Yaoguo Li. "Subspace linear inverse method." Inverse Problems 10, no. 4 (1994): 915–35. http://dx.doi.org/10.1088/0266-5611/10/4/011.

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8

D??Dârlat, D., M. Chirtoc, C. Nema??u, R. M. Cândea, and D. Bicanic. "Inverse Photopyroelectric Detection Method." physica status solidi (a) 121, no. 2 (1990): K231—K234. http://dx.doi.org/10.1002/pssa.2211210259.

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9

Keneskyzy, K., та S. B. Yeskermes. "Метод машинного обучения для обратных задач теплопроводности". INTERNATIONAL JOURNAL OF INFORMATION AND COMMUNICATION TECHNOLOGIES 2, № 1(5) (2021): 59–64. http://dx.doi.org/10.54309/ijict.2021.05.1.008.

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Investigated in this work is the potential of carrying out inverse problems with linear and non-linear behavior using machine learning methods and the neural network method. With the advent of ma-chine learning algorithms it is now possible to model inverse problems faster and more accurately. In order to demonstrate the use of machine learning and neural networks in solving inverse problems, we propose a fusion between computational mechanics and machine learning. The forward problems are solved first to create a database. This database is then used to train the machine learning and neural network algorithms. The trained algorithm is then used to determine the boundary conditions of a problem from assumed meas-urements. The proposed method is tested for the linear/non-linear heat conduction problems in which the boundary conditions are determined by providing three, four, and five temperature measurements. This re-search demonstrates that the proposed fusion of computational mechanics and machine learning is an effec-tive way of tackling complex inverse problems.

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10

Wolff, Mareille, and Jens Bange. "Inverse method as an analysing tool for airborne measurements." Meteorologische Zeitschrift 9, no. 6 (2000): 361–76. http://dx.doi.org/10.1127/metz/9/2000/361.

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11

Nedzhibov, Gyurhan. "Inverse Iterative Methods for Solving Nonlinear Equations." Mathematical and Software Engineering 1, no. 1 (2015): 6–11. https://doi.org/10.5281/zenodo.7365015.

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In this work we present an approach for obtaining new iterative methods for solving nonlinear equations. This approach can be applicable to arbitrary iterative process which is linearly or quadratically convergent. Analysis of convergence of the new methods demonstrates that the new method preserve the convergence conditions of primitive functions. Numerical examples are given to illustrate the efficiency and performance of presented methods.

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12

Venkata Sai Jitin, Jami Naga, and Atul Ramesh Bhagat. "Inverse conduction method using finite difference method." IOP Conference Series: Materials Science and Engineering 377 (June 2018): 012015. http://dx.doi.org/10.1088/1757-899x/377/1/012015.

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13

Hendriko, Hendriko, Nurkhamdi Nurkhamdi, Jajang Jaenudin, and Imam M. Muthahar. "Analytical Based Inverse Kinematics Method for 5-axis Delta Robot." International Journal of Materials, Mechanics and Manufacturing 6, no. 4 (2018): 264–67. http://dx.doi.org/10.18178/ijmmm.2018.6.4.388.

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14

Limache, Alejandro C. "Inverse method for airfoil design." Journal of Aircraft 32, no. 5 (1995): 1001–11. http://dx.doi.org/10.2514/3.46829.

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15

Zhou, Mi, and Hairui Liu. "Inverse HuaLuogeng’s “Exception Set” Method." Journal of Physics: Conference Series 1593 (July 2020): 012004. http://dx.doi.org/10.1088/1742-6596/1593/1/012004.

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16

Lam, Chi-Hang, and Leonard M. Sander. "Inverse method for interface problems." Physical Review Letters 71, no. 4 (1993): 561–64. http://dx.doi.org/10.1103/physrevlett.71.561.

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17

Tapia, Richard A., J. E. Dennis, and Jan P. Schäfermeyer. "Inverse, Shifted Inverse, and Rayleigh Quotient Iteration as Newton's Method." SIAM Review 60, no. 1 (2018): 3–55. http://dx.doi.org/10.1137/15m1049956.

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18

Chew, W. C., Y. M. Wang, G. Otto, D. Lesselier, and J. C. Bolomey. "On the inverse source method of solving inverse scattering problems." Inverse Problems 10, no. 3 (1994): 547–53. http://dx.doi.org/10.1088/0266-5611/10/3/004.

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19

Kyrchei, Ivan I. "Determinantal Representations of the Core Inverse and Its Generalizations with Applications." Journal of Mathematics 2019 (October 1, 2019): 1–13. http://dx.doi.org/10.1155/2019/1631979.

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In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.

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20

Amat, Sergio, Sonia Busquier, Miguel Ángel Hernández-Verón, and Ángel Alberto Magreñán. "On High-Order Iterative Schemes for the Matrix pth Root Avoiding the Use of Inverses." Mathematics 9, no. 2 (2021): 144. http://dx.doi.org/10.3390/math9020144.

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This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first method, an approximation of the matrix pth root. We analyze the computational cost and the convergence of this family of methods. Finally, we introduce several numerical examples in order to check the performance of this combination of schemes. We conclude that the method without inverse emerges as a good alternative since a similar numerical behavior with smaller computational cost is obtained.

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21

Amat, Sergio, Sonia Busquier, Miguel Ángel Hernández-Verón, and Ángel Alberto Magreñán. "On High-Order Iterative Schemes for the Matrix pth Root Avoiding the Use of Inverses." Mathematics 9, no. 2 (2021): 144. http://dx.doi.org/10.3390/math9020144.

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This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first method, an approximation of the matrix pth root. We analyze the computational cost and the convergence of this family of methods. Finally, we introduce several numerical examples in order to check the performance of this combination of schemes. We conclude that the method without inverse emerges as a good alternative since a similar numerical behavior with smaller computational cost is obtained.

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22

Yang, Inchul, Woo Hoon Jeon, and Jaepil Moon. "A study on a distance based coordinate calculation method using Inverse Haversine Method." Journal of Digital Contents Society 20, no. 10 (2019): 2097–102. http://dx.doi.org/10.9728/dcs.2019.20.10.2097.

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23

Aliev, Araz, Khanlar Hamzaev, Nigar Ismayilova, Eldar Jahangirbayov, Farid Jafarov, and Rahman Mammadov. "PARALLEL NUMERICAL METHOD OF AN INVERSE PROBLEM OF DOUBLE-PHASED FILTRATION." Azerbaijan Journal of High Performance Computing 2, no. 1 (2019): 75–81. http://dx.doi.org/10.32010/26166127.2019.2.1.75.81.

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24

Dominici, Diego. "Nested derivatives: a simple method for computing series expansions of inverse functions." International Journal of Mathematics and Mathematical Sciences 2003, no. 58 (2003): 3699–715. http://dx.doi.org/10.1155/s0161171203303291.

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We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the firstNterms of the series. We show several examples of its application in calculating the inverses of some special functions.

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25

Román, Nelson García, Pedro Costa Do Santos, and Pedro Henrique de Almeida Konzen. "{ANN-MoC method for the inverse problem of source characterization." Ciência e Natura 47, esp. 1 (2025): e89819. https://doi.org/10.5902/2179460x89819.

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Inverse problems of neutral particle transport have significant applications in engineering and medicine. In this study, we present a new application of the ANN-MoC method to solve inverse problems of source characterization. It involves estimating the source parameters based on measurements of particle density at the boundaries of a one-dimensional computational domain. In summary, the method employs an artificial neural network (ANN) as a regression model. The neural network is trained using data generated from solutions of the method of characteristics (MoC) for the associated direct transport problem. Results of three test cases are presented. In the first, we highlight the advantage of preprocessing the input data. For all cases, sensibility tests are provided to study the advantages and limitations of the proposed approach in solving inverses problems with noisy data.

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26

Soleymani, F., and Predrag S. Stanimirović. "A Higher Order Iterative Method for Computing the Drazin Inverse." Scientific World Journal 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/708647.

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A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper.

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27

Yang, Fan, and Wei Zhu Yang. "Data Interpolation Methods by Inverse Distance Weighted Average Method between Multidisciplines." Advanced Materials Research 1044-1045 (October 2014): 620–23. http://dx.doi.org/10.4028/www.scientific.net/amr.1044-1045.620.

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In this article, to handle data exchange between different grid systems efficiently and accuracy, the accuracy of inverse distance weighted average method is researched by different searching radius and exponent parameter. The result is compared with other two interpolation methods, radial basis function interpolation and local triangular projection method. The result shows that the search radius and exponential parameter of inverse distance weighted average interpolation method have not significant influence on interpolation result when radius is large.

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28

A. Gravvanis, George, and Christos K. Filelis-Papadopoulos. "On the multigrid cycle strategy with approximate inverse smoothing." Engineering Computations 31, no. 1 (2014): 110–22. http://dx.doi.org/10.1108/ec-03-2012-0055.

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Purpose – The purpose of this paper is to propose multigrid methods in conjunction with explicit approximate inverses with various cycles strategies and comparison with the other smoothers. Design/methodology/approach – The main motive for the derivation of the various multigrid schemes lies in the efficiency of the multigrid methods as well as the explicit approximate inverses. The combination of the various multigrid cycles with the explicit approximate inverses as smoothers in conjunction with the dynamic over/under relaxation (DOUR) algorithm results in efficient schemes for solving large sparse linear systems derived from the discretization of partial differential equations (PDE). Findings – Application of the proposed multigrid methods on two-dimensional boundary value problems is discussed and numerical results are given concerning the convergence behavior and the convergence factors. The results are comparatively better than the V-cycle multigrid schemes presented in a recent report (Filelis-Papadopoulos and Gravvanis). Research limitations/implications – The limitations of the proposed scheme lie in the fact that the explicit finite difference approximate inverse matrix used as smoother in the multigrid method is a preconditioner for specific sparsity pattern. Further research is carried out in order to derive a generic explicit approximate inverse for any type of sparsity pattern. Originality/value – A novel smoother for the geometric multigrid method is proposed, based on optimized banded approximate inverse matrix preconditioner, the Richardson method in conjunction with the DOUR scheme, for solving large sparse linear systems derived from finite difference discretization of PDEs. Moreover, the applicability and convergence behavior of the proposed scheme is examined based on various cycles and comparative results are given against the damped Jacobi smoother.

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29

Xu, Qi Hua, Shuai Geng, and Jiao Meng. "SVM Inverse Control Method to Nonlinear Systems." Advanced Materials Research 765-767 (September 2013): 1974–78. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.1974.

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In recent years, inverse system method has been achieved some progress. However, it needs not only deterministic mathematical model but also analytical expression of the inverse system. They are often not able to be realized for most of the actual control systems. Therefore, it is necessary to combine the inverse system method and the intelligent control methods which are not relied on or not entirely relied on precise model in order to overcome its "bottleneck" in practical application. The application of support vector machine in inverse system method is mainly studied in this paper. Firstly, the rigorous theory of inverse system method is introduced. Secondly, SVM inverse control method is described. Finally, the additional controller is designed to complete the closed-loop control of the pseudo linear systems. Through simulation in MATLAB, the result shows that the method in this paper is effective and feasible.

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30

Ekaterina, Gribanova. "DEVELOPMENT OF ITERATIVE ALGORITHMS FOR SOLVING THE INVERSE PROBLEM USING INVERSE CALCULATIONS." Eastern-European Journal of Enterprise Technologies 3, no. 4 (105) (2020): 27–34. https://doi.org/10.15587/1729-4061.2020.205048.

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Iterative algorithms for solving the inverse problem, presented as a quadratic programming problem, developed by modifying algorithms based on the inverse calculation mechanism are proposed. Iterative algorithms consist in a sequential change of the argument values using iterative formulas until the function reaches the value that most corresponds to the constraint. Two solutions are considered: by determining the shortest distance to the line of the given level determined by the constraint, and by moving along the gradient. This approach was also adapted to solve more general nonlinear programming optimization problems. The solution of four problems is considered: formation of production output and storage costs, optimization of the securities portfolio and storage costs for the given volume of purchases. It is shown that the solutions obtained using iterative algorithms are consistent with the result of using classical methods (Lagrange multiplier, penalty), standard function of the MathCad package. In this case, the greatest degree of compliance was obtained using the method based on constructing the level line; the method based on moving along the gradient is more universal. The advantage of the algorithms is a simpler computer implementation of iterative formulas, the ability to get a solution in less time than known methods (for example, the penalty method, which requires multiple optimizations of a modified function with a change in the penalty parameter). The algorithms can also be used to solve other nonlinear programming problems of the presented kind. The paper can be useful for specialists when solving problems in the field of economics, as well as developing decision support systems

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31

Favorite, J. A., and R. Sanchez. "An inverse method for radiation transport." Radiation Protection Dosimetry 116, no. 1-4 (2005): 482–85. http://dx.doi.org/10.1093/rpd/nci204.

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32

Pearson, D. B., and P. L. I. Skelton. "The Inverse Method for Transfer Matrices." Journal of the London Mathematical Society s2-40, no. 3 (1989): 476–89. http://dx.doi.org/10.1112/jlms/s2-40.3.476.

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33

Gao, He, and Jie Zhu. "Inverse design method for acoustic metamaterials." Journal of the Acoustical Society of America 146, no. 4 (2019): 2828. http://dx.doi.org/10.1121/1.5136799.

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34

Voller, V. R. "ENTHALPY METHOD FOR INVERSE STEFAN PROBLEMS." Numerical Heat Transfer, Part B: Fundamentals 21, no. 1 (1992): 41–55. http://dx.doi.org/10.1080/10407799208944921.

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35

Shamma, J. S., and D. E. Whitney. "A Method for Inverse Robot Calibration." Journal of Dynamic Systems, Measurement, and Control 109, no. 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.

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36

Soykasap, Ömer. "Inverse method in tilt-rotor optimization." Aerospace Science and Technology 5, no. 7 (2001): 437–44. http://dx.doi.org/10.1016/s1270-9638(01)01117-8.

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37

Maniatty, Antoinette, and Nicholas Zabaras. "Method for Solving Inverse Elastoviscoplastic Problems." Journal of Engineering Mechanics 115, no. 10 (1989): 2216–31. http://dx.doi.org/10.1061/(asce)0733-9399(1989)115:10(2216).

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38

Zamov, N. K. "Maslov's inverse method and decidable classes." Annals of Pure and Applied Logic 42, no. 2 (1989): 165–94. http://dx.doi.org/10.1016/0168-0072(89)90053-5.

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39

Osipov, A. I., L. A. Shelepin, and S. L. Shelepin. "Inverse problem method in laser physics." Journal of Russian Laser Research 26, no. 2 (2005): 116–36. http://dx.doi.org/10.1007/s10946-005-0011-7.

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40

Pshenichnyi, B. N., and L. A. Sobolenko. "Linearization method for inverse convex programming." Cybernetics and Systems Analysis 31, no. 6 (1995): 852–62. http://dx.doi.org/10.1007/bf02366622.

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41

Leonov, A. S. "The minimal pseudo-inverse matrix method." USSR Computational Mathematics and Mathematical Physics 27, no. 4 (1987): 107–17. http://dx.doi.org/10.1016/0041-5553(87)90019-x.

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42

Dinariev, O. Yu, and A. B. Mosolov. "Inverse problem method for Burgers' equation." Ukrainian Mathematical Journal 41, no. 7 (1989): 827–29. http://dx.doi.org/10.1007/bf01060703.

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43

Liu, Juan, and Jiguang Sun. "Extended sampling method in inverse scattering." Inverse Problems 34, no. 8 (2018): 085007. http://dx.doi.org/10.1088/1361-6420/aaca90.

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44

Ternovskii, V. V., and M. M. Khapaev. "Inverse problem method in optimal control." Doklady Mathematics 83, no. 3 (2011): 357–60. http://dx.doi.org/10.1134/s1064562411030318.

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45

Liu, Yi, Fang-Fang Yin, and Qinghuai Gao. "Variation method for inverse treatment planning." Medical Physics 26, no. 3 (1999): 356–63. http://dx.doi.org/10.1118/1.598525.

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46

Zhang, Yuan, Zengqiang Chen, Peng Yang, and Zhuzhi Yuan. "Nonlinear system compound inverse control method." Journal of Control Theory and Applications 3, no. 3 (2005): 218–22. http://dx.doi.org/10.1007/s11768-005-0038-x.

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47

Daripa, Prabir K., and Lawrence Sirovich. "An inverse method for subcritical flows." Journal of Computational Physics 63, no. 2 (1986): 311–28. http://dx.doi.org/10.1016/0021-9991(86)90196-8.

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48

Kasimu Juma Ahmed, Bashir Saidu Musa, Mustapha Muhammad Lamido, Shehu Adamu, Muhammad Bello Mustapha, and Ado Bappayo. "Inverse Method for Order n Matrix." World Journal of Advanced Research and Reviews 26, no. 2 (2025): 4148–57. https://doi.org/10.30574/wjarr.2025.26.2.1978.

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The power of matrix algebra was seen not only in applied mathematics, applied sciences, engineering but also in economics, sociology, modern psychology and industrial management (i.e., system of linear equation, cryptography, optics, signal processing, image processing, graph theory, Machine Learning, Data Science etc.). In practice the matrix inverse methods is suitable only for non-singular small system because the higher the size of the system the more difficult finding the inverse of the system even with the help of software/application. With experience we were able to find the inverse of order 4, 5, … , n matrix with ease and also verified the method by computing .

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49

Zhu, Tao, Shoune Xiao, Guangwu Yang, Weihua Ma, and Zhixin Zhang. "AN INVERSE DYNAMICS METHOD FOR RAILWAY VEHICLE SYSTEMS." TRANSPORT 29, no. 1 (2013): 107–14. http://dx.doi.org/10.3846/16484142.2013.789979.

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The wheel–rail action will obviously be increased during the vehicles in high-speed operation state. However, in many practical cases, direct measurement of the wheel–rail contact forces cannot be performed with traditional procedures and transducers. An inverse mathematical dynamic model for the estimation of wheel–rail contact forces from measured accelerations was developed. The inverse model is a non-iteration recurrence method to identify the time history of input excitation based on the dynamic programming equation. Furthermore, the method overcomes the weakness of large fluctuations which exist in current inverse techniques. Based on the inverse dynamic model, a high-speed vehicle multibody model with twenty-seven Degree of Freedoms (DOFs) is established. With the measured responses as input, the inverse vehicle model can not only identify the responses in other parts of vehicle, but also identify the vertical and lateral wheel–rail forces respectively. Results from the inverse model were compared with experiment data. In a more complex operating condition, the inverse model was also compared with results from simulations calculated by SIMPACK.

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50

Huang, Qing Qing, Guang Feng Chen, Jiang Hua Li, and Xin Wei. "Simulation on Trajectory Planning of 6R Manipulator Based on the Shortest Distance Criterion." Applied Mechanics and Materials 602-605 (August 2014): 942–45. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.942.

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This paper concerns the trajectory planning and simulation for 6R Manipulator. First, algebraic method was used to deduce the forward and inverse kinematics of 6R manipulator. All inverse solutions were expressed in atan2 to eliminate redundant roots to get the corresponding inverse formula. For the trajectory planning of manipulator in Cartesian space, using the cubic spline interpolation to get the drive function of joint, getting a unique solution from eight group inverses by the shortest distance criterion, and then obtained the actual end-effector trajectory. Using Matlab to verify the proposed trajectory planning method, validated results show that the proposed algorithm is feasible and effective.

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