New algorithms for numerically solving a class of bordered tridiagonal systems of linear equations

摘要

In this paper, we consider the solution of opposite-bordered tridiagonal (OBT) systems of linear equations. Two novel numerical algorithms are presented for solving an OBT system of n equations in linear time. The first algorithm is based on any fast and reliable tridiagonal linear solver. If users have the codes for tridiagonal solvers, then the algorithm can be readily implemented by a slight modification. The second algorithm is based on a certain type of column operation that transforms the original OBT system of linear equations in terms of a quasi-lower triangular system of linear equations. The corresponding results in this paper can be directly obtained for solving singly-bordered tridiagonal systems of linear equations. (C) 2019 Elsevier Ltd. All rights reserved.