Systolic implementation of preconditioned conjugate gradient method in adaptive transversal filters

Abstract

The Preconditioned Conjugate Gradient (PCG) Method is used for solving systems of linear equations with symmetric positive definite matrix. A two-dimensional processor array implementation is obtained by using the data dependence method. The method cannot be implemented directly because the algorithm is a three step procedure, for each iteration. Obtaining a regular data flow between the different stages in the algorithm is a difficult problem to be solved. Special techniques are introduced for this purpose such as broadcast elimination, synchronization between stages, introduction of new variables, pipelining the variables and other reindexing techniques. The implementation of the PCG method is tested on Sequent Balance B-8000 parallel computer at Loughborough University of Technology. The systolic array is simulated using Occam and transputter array simulator.