Block-row and block-column iterative algorithms for solving linear matrix equation

Using tools like the Kronecker product and the vector operator, various Sylvester matrix equations can always be converted into the form A x = f , motivating us to investigate the algorithm for solving the linear matrix equation A x = f . By dividing the coefficient matrix A into row blocks or colum...

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Bibliographic Details
Published in:Computational & applied mathematics Vol. 42; no. 4
Main Authors: Wang, Wenli, Qu, Gangrong, Song, Caiqin, Liu, Duo
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2023
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Accelerated block-column iterative algorithm
15A24
65F10
15A21
Gradient-based iterative algorithm
Linear matrix equation
Block-row iterative algorithm
Block-column iterative algorithm
ISSN:2238-3603, 1807-0302
Online Access:Get full text
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Summary:Using tools like the Kronecker product and the vector operator, various Sylvester matrix equations can always be converted into the form A x = f , motivating us to investigate the algorithm for solving the linear matrix equation A x = f . By dividing the coefficient matrix A into row blocks or column blocks, a block-row iterative (BRI) algorithm, a block-column iterative (BCI) algorithm and an accelerated block-column iterative (ABCI) algorithm are developed to solve A x = f . It is successfully proved that the numerical solution produced by the proposed algorithms can converge to the exact solution for any given initial vector under appropriate conditions. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed algorithms.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-023-02312-y