Divide and Conquer: A New Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations

Bondeli, S_, Divide and conquer: a parallel algorithm for the solution of a tridiagonal linear system of equations, Parallel Comput ing 17 (1991) 419-434_ 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 flexible, permits multiprocessing or a combinat ion 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 F X/ 8 , and on a Sequent Symmetry S81b, as well as comparisons with the cyclic reduction algorithm and Gauss ian elimination will be presented. Finally, numerical results are given. Keywords_ Linear algebra; tridiagonal systems; divide and conquer; timing results_