On deflated CGW methods for solving nonsymmetric positive definite linear systems.
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| Title: | On deflated CGW methods for solving nonsymmetric positive definite linear systems. |
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| Authors: | Du, Kui1 (AUTHOR) kuidu@xmu.edu.cn, Fan, Jia-Jun2 (AUTHOR) jiajunfan@stu.xmu.edu.cn, Wang, Fang2 (AUTHOR) fangwang@stu.xmu.edu.cn |
| Source: | Calcolo. Jun2025, Vol. 62 Issue 2, p1-21. 21p. |
| Subjects: | Linear systems, Lanczos method, Iterative methods (Mathematics), Empirical research, Matrices (Mathematics), Linear algebra, Eigenvalue equations |
| Abstract: | We propose a deflated CGW method (D-CGW) to approximate the solution of nonsymmetric positive definite linear systems. D-CGW utilizes some eigenspaces, and can be useful in cases when the slow convergence is due to a small number of eigenvalues with large magnitude in the generalized eigenvalue problem S x = λ H x , where S and H represent the skew-symmetric and symmetric parts of the coefficient matrix of nonsymmetric positive definite linear systems, respectively. Additionally, we introduce a skew-symmetric Lanczos method with deflated restarting, referred to as S 2 Lan-DR, which simultaneously solves nonsymmetric positive definite linear systems and computes eigenspaces. The computed eigenspaces can be used in D-CGW to solve successive linear systems. Numerical experiments are given to illustrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | We propose a deflated CGW method (D-CGW) to approximate the solution of nonsymmetric positive definite linear systems. D-CGW utilizes some eigenspaces, and can be useful in cases when the slow convergence is due to a small number of eigenvalues with large magnitude in the generalized eigenvalue problem S x = λ H x , where S and H represent the skew-symmetric and symmetric parts of the coefficient matrix of nonsymmetric positive definite linear systems, respectively. Additionally, we introduce a skew-symmetric Lanczos method with deflated restarting, referred to as S 2 Lan-DR, which simultaneously solves nonsymmetric positive definite linear systems and computes eigenspaces. The computed eigenspaces can be used in D-CGW to solve successive linear systems. Numerical experiments are given to illustrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 00080624 |
| DOI: | 10.1007/s10092-025-00646-z |
