Stability Issues of the Wang's Partitioning Algorithm for Banded and Tridiagonal Linear Systems
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Stability of a Parallel Partitioning Algorithm for Special Classes of Banded Linear Systems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Stability of block LU factorization for block tridiagonal matrices
Computers & Mathematics with Applications
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Componentwise error analysis for a parallel partitioning algorithm for tridiagonal systems is presented. Bounds on the equivalent perturbations are obtained, depending on three constants. Then bounds on the forward error are presented as well, depending on two types of condition numbers. Estimates on the first constant come directly from the roundoff error analysis of the tridiagonal Gaussian elimination [N. Higham, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 521--530]. In the present paper, the second and third constants are bounded for some special classes of matrices, i.e., diagonally dominant (row or column), symmetric positive definite, M-matrices, and totally nonnegative.One of the features of the analysis is that the exact forward and backward errors are bounded, not just their first order approximations, with respect to the machine precision. In all the bounds, the linear terms are given separately to show that the terms of higher order are small enough.