The Solution of Certain Banded Systems of Linear Equations Using the Folding Algorithm

Abstract

The problem of solving a banded system of linear equations Ax = b occurs frequently in the numerical solution of partial and ordinary differential equations. In the case when the matrix A is banded with semi-bandwidth p and the elements satisfy the relationship a_{i, j} = a_{n−i+1, n−j+1}, simple techniques of folding enable a more compact version of Gaussian elimination to be constructed which possess advantages of efficiency and accuracy.