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

• Published in: Trends in Computational and Applied Mathematics Vol. 24; no. 1; pp. 177 - 190
• Main Authors: Almeida, C. G., Remigio, S. A. E.
• Format: Journal Article
• Language: English
• Published: Sociedade Brasileira de Matemática Aplicada e Computacional - SBMAC 01.03.2023; Sociedade Brasileira de Matemática Aplicada e Computacional
• Subjects: Crout's method; MATHEMATICS; MATHEMATICS, APPLIED; Toeplitz tridiagonal matrix; tridiagonal and diagonally dominant matrix; tridiagonal and diagonally dominant matrix; Toeplitz tridiagonal matrix; Crout’s method
• ISSN: 2676-0029; 2676-0029
• DOI: 10.5540/tcam.2022.024.01.00177

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.