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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Vydané v:	Optimal control applications & methods Ročník 45; číslo 4; s. 1593 - 1602
Hlavný autor:	Bayoumi, Ahmed M. E.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Hoboken, USA John Wiley & Sons, Inc 01.07.2024
Predmet:	convergence gradient iterative algorithm Jacobi‐gradient iterative algorithm matrix equation shift‐splitting Jacobi‐gradient
ISSN:	0143-2087, 1099-1514
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Shrnutí:	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