THE PRECONDITIONED CONJUGATE GRADIENT METHOD ON THE CONNECTION MACHINE
Charles Tong · International Journal of High Speed Computing · 1989
This paper presents the results of the Connection Machine implementation of a number of preconditioners for the preconditioned conjugate gradient method. The preconditioners implemented include those based on the incomplete LU factorization, the modified incomplete LU factorization, the symmetric successive overrelaxation, and others such as several polynomial preconditioners and the hierarchical basis preconditioner. Results based on numerical experiments show that both the degree of parallelism inherent in a preconditioner and its convergence rate improvement play important roles on the overall execution time performance on parallel computers. Factors that affect the performance of the preconditioners will also be discussed. We conclude that to search for the best preconditioner on a parallel machine, we have to consider the tradeoffs between fast convergence rate and high degree of parallelism as well as the architecture of the target parallel computer.