Stability of Block LDLT Factorization of a Symmetric Tridiagonal Matrix
نویسندگان
چکیده
For symmetric indeenite tridiagonal matrices, block LDL T factorization without interchanges is shown to have excellent numerical stability when a pivoting strategy of Bunch is used to choose the dimension (1 or 2) of the pivots.
منابع مشابه
Stability of block LDL factorization of a symmetric tridiagonal matrix
For symmetric inde®nite tridiagonal matrices, block LDL factorization without interchanges is shown to have excellent numerical stability when a pivoting strategy of Bunch is used to choose the dimension (1 or 2) of the pivots. Ó 1999 Elsevier Science Inc. All rights reserved. AMS classi®cation: 65F05; 65G05
متن کاملMultiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
In this paper we present an O(nk) procedure, Algorithm MR3, for computing k eigenvectors of an n× n symmetric tridiagonal matrix T . A salient feature of the algorithm is that a number of different LDLt products (L unit lower triangular, D diagonal) are computed. In exact arithmetic each LDLt is a factorization of a translate of T . We call the various LDLt products representations (of T ) and,...
متن کاملStable Factorizations of Symmetric Tridiagonal and Triadic Matrices
We call a matrix triadic if it has no more than two nonzero off-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider LXLT factorizations of symmetric triadic matrices, where L is unit lower triangular and X is diagonal, block diagonal with 1×1 and 2×2 blocks, or the identity with L lower triangular. We prove that with diagonal pivoting, th...
متن کاملParallel Numerical Algorithms for Symmetric Positive Definite Linear Systems
We give a matrix factorization for the solution of the linear system Ax = f , when coefficient matrix A is a dense symmetric positive definite matrix. We call this factorization as "WW T factorization". The algorithm for this factorization is given. Existence and backward error analysis of the method are given. The WDWT factorization is also presented. When the coefficient matrix is a symmetric...
متن کاملOrthogonal Eigenvectors and Relative Gaps
This paper presents and analyzes a new algorithm for computing eigenvectors of symmetric tridiagonal matrices factored as LDLt, with D diagonal and L unit bidiagonal. If an eigenpair is well behaved in a certain sense with respect to the factorization, the algorithm is shown to compute an approximate eigenvector which is accurate to working precision. As a consequence, all the eigenvectors comp...
متن کامل