A fast parallel algorithm for the solution of tridiagonal linear systems

Abstract

We present a parallel algorithm for the solution of tridiagonal linear systems based on the method of partitioning and backward elimination. A given N × N system is partitioned into r blocks each of size n × n (N = rn n even). Within each block the system is rewritten by collecting pairs of equations from the top and bottom (written backwards); this makes it suitable to solve the subsystem by a UL-factorization of its coefficient matrix. Once a core system of size 2r × 2r has been solved, solutions of the r subsystems can be computed in parallel. Interestingly, the serial arithmetical operations count for the present algorithm is 0(1612;N); this makes it faster than the quadrant interlocking factorization method of Chawla and Passi [1], the partitioning method of Wang [7] and cyclic reduction (see Hockney and Jesshope [6, p. 479]), each of which has a serial count of 0(17N).

Keywords:

• Tridiagonal linear systems
• partitioning
• backward Gaussian elimination
• parallel algorithm

C.R.Categories:

• G.1.3
• G.1.0