A shift‐splitting Jacobi‐gradient iterative algorithm for solving the matrix equation A𝒱−𝒱‾B=C

To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi‐gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift‐splitting Jacobi‐gradient iterative (SSJGI) algorithm for solving the matrix equation A𝒱−𝒱‾B=C is presented in this paper, which is based...

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Bibliographic Details
Published in:Optimal control applications & methods Vol. 45; no. 4; pp. 1593 - 1602
Main Author: Bayoumi, Ahmed M. E.
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.07.2024
Subjects:
convergence
gradient iterative algorithm
Jacobi‐gradient iterative algorithm
matrix equation
shift‐splitting Jacobi‐gradient
ISSN:0143-2087, 1099-1514
Online Access:Get full text
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Summary:To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi‐gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift‐splitting Jacobi‐gradient iterative (SSJGI) algorithm for solving the matrix equation A𝒱−𝒱‾B=C is presented in this paper, which is based on the splitting of the coefficient matrices. The proposed algorithm converges to the exact solution for any initial value with some conditions. To demonstrate the effectiveness of the SSJGI algorithm and to compare it to the GI algorithm and the JGI algorithm [Bayoumi, Appl Math Inf Sci, 2021], numerical examples are provided. In this paper, a novel algorithm called the shift‐splitting Jacobi‐gradient iterative (SSJGI) algorithm is introduced to enhance the convergence of the gradient iterative (GI) algorithm and the Jacobi‐gradient iterative (JGI) algorithm. This algorithm is based on the splitting of the coefficient matrices.
ISSN:0143-2087
1099-1514
DOI:10.1002/oca.3112