An algorithm for the solution of certain tridiagonal systems of linear equations
D. J. Evans · The Computer Journal · 1972
Recently, interest in new fast direct methods for solving finite difference approximations to the standard partial differential equations of Mathematical Physics has been renewed by the introduction of the fast Fourier transform and Buneman's variant of the cyclic odd-even reduced algorithms. In this paper, a new algorithm, i.e., the reverse triangular factorisation and expansion (ReTriFE) method is introduced and developed to solve the tridiagonal systems occurring in the numerical solution of certain elliptic partial difference equations over regions involving Dirichlet boundary conditions. Discussions on the error analysis of the algorithm is included and generalisations to block tridiagonal matrix schemes indicated.