A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices

As a generalization of k-tridiagonal matrices, many variations of (p,q)-tridiagonal matrices have attracted much attention over the years. In this paper, we present an efficient algorithm for numerically computing the inverses of n-square (p,q)-tridiagonal matrices under a certain condition. The algorithm is based on the combination of a bidiagonalization approach which preserves the banded structure and sparsity of the original matrix, and a recursive algorithm for inverting general lower bidiagonal matrices. Some numerical results with simulations in MATLAB implementation are provided in order to illustrate the accuracy and efficiency of the proposed algorithms, and its competitiveness with MATLAB built-in function.