John Wiley & Sons, Ltd. Chichester, UK 10.1002/(ISSN)2040-7947 2040-7939 2040-7947 International Journal for Numerical Methods in Biomedical Engineering Int. J. Numer. Meth. Biomed. Engng. 10.1002/cnm.v26:6 26 6 June 2010 10.1002/cnm.1172 Communications in Numerical Methods in Engineering – Articles published in this section are of a more general engineering nature and do not necessarily have biomedical applications Communications in Numerical Methods in Engineering – Articles published in this section are of a more general engineering nature and do not necessarily have biomedical applications Copyright © 2008 John Wiley & Sons, Ltd. 752 759 Department of Aerospace Engineering, The University of Michigan, 1320 Beal Avenue, Ann Arbor, MI 48109, U.S.A. Variant of the Thomas Algorithm for opposite‐bordered tridiagonal systems of equations VARIANT OF THE THOMAS ALGORITHM Alexandre Martin almar@umich.edu Iain D. Boyd Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109, U.S.A. linear solver Thomas Algorithm elementary column operations Government of Québec Fonds de recherche sur la nature et les technologies (NATEQ) NASA Constellation University Institutes Program NCC3‐989 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 𝒪(n) operations, instead of 𝒪(n3) . 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.