Divide and conquer: A new parallel algorithm for the solution of a tridiagonal linear system of equations

Abstract

We describe a divide and conquer algorithm which solves linear tridiagonal systems with one right-hand side, especially suited for parallel computers. The algorithm is very flexible, permits multiprocessing or a combination of vector and multiprocessor implementations, and is adaptable to a wide range of parallelism granularities. This algorithm can also be combined with recursive doubling, cyclic reduction or Wang’s partition method, in order to increase the degree of parallelism and vectorizability. The divide and conquer method will be explained. Some results of time measurements on a CRAY X-MP/28, on an Alliant FX/8 and on a Sequent Symmetry S81b as well as comparisons with the cyclic reduction algorithm and Gaussian elimination will be presented.