Tridiagonal interval matrices are relevant in diverse applications, especially in dealing with parameter estimation, optimization and circuit analysis uncertainties. This research paper aims to improve the computational efficiency of obtaining the inverse of a general tridiagonal interval matrix. This matrix is pivotal in electric circuit analysis. We achieve this by employing interval arithmetic operations in the LU decomposition process, enabling effective handling of circuit parameter uncertainties. This approach generates an inverse interval matrix that addresses uncertainties in circuit analyses.

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

. Square matrices, A , strictly diagonally dominant belong to an important class of in-vertible matrices that have an LU decomposition. We will present in this work new non singularity criteria based on Crout’s method for non strictly diagonally dominant pentadiagonal (or tridiagonal) matrices that admit an LU decomposition. These criteria are simple and easy to implement. There are many papers on this subject in the literature. However, the results that ensure non singularity of A usually depend on the conditions that are not promptly obtained. Palavras-chave . Crout’s method, pentadiagonal matrices, non strictly diagonally dominant matrices

Non singularity criteria for non strictly diagonally dominant pentadiagonal matrices

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.

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

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.

Sobre matrizes pentadiagonais não estritamente diagonais dominantes

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

Sobre matrizes pentadiagonais não estritamente diagonais dominantes