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

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  • Kamra, Rabia
  • Rao, S. Chandra Sekhara

Abstract

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.

Suggested Citation

  • Kamra, Rabia & Rao, S. Chandra Sekhara, 2021. "A stable parallel algorithm for block tridiagonal toeplitz–block–toeplitz linear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1415-1440.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:1415-1440
    DOI: 10.1016/j.matcom.2021.07.019
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