On non strictly diagonally dominant pentadiagonal matrices
DOI:
https://doi.org/10.35819/remat2024v10i2id7012Keywords:
Crout's method, pentadiagonal matrix, non strictly diagonally dominant matricesAbstract
Based on Crout's method, we will present, in this work, new non singularity criteria and sufficient conditions for existence of the LU factorization, for non strictly diagonally dominant pentadiagonal matrices. Crout's method is a recursive process of n stages that obtains the factorization A = LU of a pentadiagonal matrix of order n. In this recursive process of obtaining both the lower triangular matrix L and the upper triangular matrix U, the parameters alpha_i, 1 <= i <= n, must be non-zero to ensure that det(A) neq 0 and A = LU. Crout's recursive method is replaced by the analysis of sufficient conditions that can be verified simultaneously with low computational cost.
Downloads
References
ALMEIDA, C. G. de; REMIGIO, S. A. E. Non singularity criteria for non strictly diagonally dominant pentadiagonal matrices. In: CONGRESSO NACIONAL DE MATEMÁTICA APLICADA E COMPUTACIONAL, LXIII, 2023, Universidade Federal de Mato Grosso do Sul, Bonito/MS. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, v. 10, n. 1, São Paulo: SBMAC, p. 010074-1 - 010074-7, 2023. DOI: https://doi.org/10.5540/03.2023.010.01.0074.
ALMEIDA, C. G. de; REMIGIO, S. A. E. Sufficient Conditions for Existence of the LU Factorization of Toeplitz Symmetric Tridiagonal Matrices. Trends in Computational and Applied Mathematics, São Carlos, SP, v. 24, n. 1, p. 177-190, Mar. 2023. DOI: https://doi.org/10.5540/tcam.2022.024.01.00177.
BANK, Randolph E.; ROSE, Donald J. Marching algorithms for elliptic boundary value problems. I: The constant coefficient case. SIAM Journal on Numerical Analysis, v. 14, n. 5, p. 792-829, 1977. DOI: https://doi.org/10.1137/0714055.
EL-MIKKAWY, Moawwad E. A. On the inverse of a general tridiagonal matrix. Applied Mathematics and Computation, v. 150, n. 3, p. 669-679, 2004. DOI: https://doi.org/10.1016/S0096-3003(03)00298-4.
FISCHER, Charlotte F.; USMANI, Riaz A. Properties of some tridiagonal matrices and their application to boundary value problems. SIAM Journal on Numerical Analysis, v. 6, n. 1, p. 127-142, 1969. DOI: https://doi.org/10.1137/0706014.
JOHNSON, Charles Royal; MARIJUÁN, Carlos; PISONERO, Miriam. Diagonal dominance and invertibility of matrices. Special Matrices, v. 11, n. 1, p. 20220181, 2023. DOI: https://doi.org/10.1515/spma-2022-0181.
KOLOTILINA, Liliya Yurievna. Nonsingularity/singularity criteria for nonstrictly block diagonally dominant matrices. Linear Algebra and its Applications, v. 359, n. 1-3, p. 133-159, 2003. DOI: https://doi.org/10.1016/S0024-3795(02)00422-6.
MEURANT, Gérard. A review on the inverse of symmetric tridiagonal and block tridiagonal matrices. SIAM Journal on Matrix Analysis and Applications, v. 13, n. 3, p. 707-728, 1992. DOI: https://doi.org/10.1137/0613045.
ZHAO, Xi-Le; HUANG, Ting-Zhu. On the inverse of a general pentadiagonal matrix. Applied Mathematics and Computation, v. 202, n. 2, p. 639-646, 2008. DOI: https://doi.org/10.1016/j.amc.2008.03.004.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 César Guilherme de Almeida, Santos Alberto Enriquez Remigio
This work is licensed under a Creative Commons Attribution 4.0 International License.
Os autores detêm os direitos autorais dos artigos publicados e concedem à REMAT o direito de primeira publicação e distribuição de partes ou do trabalho como um todo com o objetivo de promover a revista. Os autores são autorizados a distribuir a versão publicada do artigo, como por exemplo em repositórios institucionais, desde que façam menção de publicação inicial nesta revista a partir da disponibilização do DOI do artigo.
Os artigos são publicados sob a licença Creative Commons Attribution 4.0 International License (CC BY 4.0). Isso permite que o conteúdo seja utilizado para criação de novos trabalhos, tanto para fins comerciais quanto não comerciais, desde que seja feita a devida atribuição ao autor original, conforme especificado na licença.
Última atualização: 07/02/2025, 19:22.
How to Cite
