ALGORITHM FOR SOLUTION OF CERTAIN TRIDIAGONAL SYSTEMS OF LINEAR EQUATIONS

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 factorization and expansion (ReTriFE) method is introduced and developed to solve the tridiagonal systems occurring in the numerical solution of certain elliptic partial differential equations over regions involving Dirichlet boundary conditions. Discussions on the error analysis of the algorithm is included and generalizations to block tridiagonal matrix schemes indicated.