A stable parallel algorithm for block tridiagonal toeplitz–block–toeplitz linear systems

In this paper, we present a direct parallel block WZ algorithm, named DPBWZA, for the solution of block tridiagonal toeplitz–block–toeplitz (TBT) linear system Ax=f. The algorithm is based on the proposed block WZ factorization of the coefficient matrix A. Existence of the block WZ factorization for...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics and computers in simulation Vol. 190; pp. 1415 - 1440
Main Authors: Kamra, Rabia, Rao, S. Chandra Sekhara
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2021
Subjects:
[formula omitted] factorization
Block diagonal dominance
Block tridiagonal linear system
CUDA
cuSOLVER library
Toeplitz–block–toeplitz linear system
WZ factorization
CUDA
Block tridiagonal linear system
Block diagonal dominance
cuSOLVER library
Toeplitz–block–toeplitz linear system
ISSN:0378-4754
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we present a direct parallel block WZ algorithm, named DPBWZA, for the solution of block tridiagonal toeplitz–block–toeplitz (TBT) linear system Ax=f. The algorithm is based on the proposed block WZ factorization of the coefficient matrix A. Existence of the block WZ factorization for block tridiagonal TBT block diagonally dominant matrix is proved. Error analysis of the parallel algorithm DPBWZA is presented and numerical stability of the algorithm is established. Numerical experiments are conducted to demonstrate the efficiency, stability and accuracy of the Direct Parallel Block WZ Algorithm on GPU platform. Forward and backward errors are computed and DPBWZA is found to be highly accurate, numerically stable and as efficient as the subroutine csrlsvlu of GPU accelerated cuSolverSP library. •A direct parallel block WZ algorithm for block tridiagonal toeplitz–block–toeplitz linear systems.•The present parallel algorithm is accurate and numerically stable.•As efficient as the subroutine csrlsvlu of GPU accelerated cuSolverSP library.
ISSN:0378-4754
DOI:10.1016/j.matcom.2021.07.019