A tridiagonalization-based arbitrary-stride reduction approach for (p,q)-pentadiagonal linear systems

Abstract

As a generalization of pentadiagonal matrices, $(p,q)$-pentadiagonal matrices have recently attracted considerable interest. In this paper, we first present an arbitrary-stride reduction for block diagonal linear systems composed of M-tridiagonal matrices. Building upon this reduction method and a reliable tridiagonalization process, we propose a tridiagonalization-based arbitrary-stride reduction approach for the $(p,q)$-pentadiagonal linear systems. Also, we elucidate eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction. Numerical experiments are provided to illustrate the effectiveness of our proposed approach, implementing all experiments using MATLAB programs on a computer.