Variant of the Thomas Algorithm for opposite-bordered tridiagonal systems of equations

Abstract

To solve tridiagonal systems of linear equations, the Thomas Algorithm is a much more efficient method than, for instance, Gaussian elimination. The algorithm uses a series of elementary row operations and can solve a system of n equations in ( n ) operations, instead of ( n 3 ) . Many variations of the Thomas Algorithm have been developed over the years to solve very specific near-tridiagonal matrix. However, none of these methods address the situation of a system of linear equations that could easily be solved if elementary operations on columns are applied, instead of elementary operations on rows. The present paper proposes an efficient method that allows the use of elementary column operations to solve linear systems of equations using vector multiplication techniques, such as the one proposed by Thomas. Copyright © 2008 John Wiley & Sons, Ltd.