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868 results on '"Xing, Lili"'

3. Kaczmarz-Type Methods for Solving Matrix Equations

Author

Li, Weiguo, Bao, Wendi, Xing, Lili, and Guo, Zhiwei

Subjects
Mathematics - Numerical Analysis, 65F10, 65F20, 65F30, 65F50
Abstract

In this paper, several Kaczmarz-type numerical methods for solving the matrix equation $AX=B$ and $XA=C$ are proposed, where the coefficient matrix $A$ may be full rank or rank deficient. These methods are iterative methods without matrix multiplication. Theoretically, the convergence of these methods is proved. The numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrices., Comment: arXiv admin note: text overlap with arXiv:2305.16684

Published
2023

4. A class of pseudoinverse-free greedy block nonlinear Kaczmarz methods for nonlinear systems of equations

Author

Lv, Ying, Bao, Wendi, Xing, Lili, and Li, Weiguo

Subjects
Mathematics - Numerical Analysis
Abstract

In this paper, we construct a class of nonlinear greedy average block Kaczmarz methods to solve nonlinear problems without computing the Moore-Penrose pseudoinverse. This kind of methods adopts the average technique of Gaussian Kaczmarz method and combines with the greedy strategy, which greatly reduces the amount of computation. The convergence analysis and numerical experiments of the proposed method are given. The numerical results show the effectiveness of the proposed methods.

Published
2023

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