A fast algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems

Belhaj, Skander; Hcini, Fahd; Moakher, Maher; Zhang, Y.

doi:10.1007/s10910-021-01217-7

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…Recent research continues to highlight the importance of studying Topelitz matrices, such as [3,12,13,19].…”

Section: Introductionmentioning

confidence: 99%

“…However, the authors did not present sufficient conditions for existence of the LU factorization of Toeplitz tridiagonal matrices. In 2021, Skander Belhaj et al [3] also developed in their paper a fast algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems. Numerical experiments were given in order to illustrate the validity and efciency of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Sufficient Conditions for Existence of the LU Factorization of Toeplitz Symmetric Tridiagonal Matrices

Almeida

Remigio

2023

TCAM

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The characterization of inverses of symmetric tridiagonal and block tridiagonal matrices and the development of algorithms for finding the inverse of any general non-singular tridiagonal matrix are subjects that have been studied by many authors. The results of these research usually depend on the existence of the LU factorization of a non-sigular matrix A, such that A = LU. Besides, the conditions that ensure the nonsingularity of A and its LU factorization are not promptly obtained. Then, we are going to present in this work two extremely simple sufficient conditions for existence of the LU factorization of a Toeplitz symmetric tridiagonal matrix A. We take into consideration the roots of the modified Chebyshev polynomial, and we also present an analysis based on the parameters of the Crout’s method.

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“…Recent research continues to highlight the importance of studying Topelitz matrices, such as [3,12,13,19].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sufficient Conditions for Existence of the LU Factorization of Toeplitz Symmetric Tridiagonal Matrices

Almeida

Remigio

2023

TCAM

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“…Later on this method was generalised to solve the block quasi tridiagonal Toeplitz [4]. In [5,6], a fast method for solving quasi-pentadiagonal Toeplitz linear systems was presented, which was based on solving pentadiagonal Toeplitz linear systems.…”

Section: Introductionmentioning

confidence: 99%

New algorithm for solving pentadiagonal CUPL-Toeplitz linear systems

Hcini

Zhang

2023

Comp. Appl. Math.

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A fast algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems

Abstract: In this paper, we develop a new algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems. Numerical experiments are given in order to illustrate the validity and efficiency of our algorithm.

Cited by 2 publications

References 18 publications

Sufficient Conditions for Existence of the LU Factorization of Toeplitz Symmetric Tridiagonal Matrices

Sufficient Conditions for Existence of the LU Factorization of Toeplitz Symmetric Tridiagonal Matrices

New algorithm for solving pentadiagonal CUPL-Toeplitz linear systems

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