A parallel version of the cyclic reduction algorithm on a hypercube

Abstract

The cyclic reduction algorithm is one of the fastest algorithms for the solution of tridiagonal linear systems on parallel computers. We consider an efficient version of this algorithm on distributed memory parallel computers. The basic idea is to divide the original system into subsystems which are solved almost independently. Communications are only needed for solving a tridiagonal system whose dimension is proportional to the number of processors. By utilizing a hypercube as topology of interconnection among the processors, the solution of this subsystem requires communication among neighbouring processors. The number of synchronizations is proportional to the logarithm of the number of processors. Some numerical tests are performed on a net of transputers. The parallel cyclic reduction is compared with the LU factorization algorithm, that is the fastest algorithm on a scalar computer.