On the efficient implementation of preconditioned s-step conjugate gradient methods on multiprocessors with memory hierarchy

Abstract Multiprocessor architectures combining vector and parallel processing capabilities on a two-level shared memory structure have been implemented. This memory hierarchy structure requires that numerical algorithms possess good data locality in order to achieve high performance rates. The s-step Conjugate Gradient method (s-CG) is a generalization of the standard CG method with improved data locality and parallel properties. Here we show how to implement efficiently the Incomplete Cholesky and Polynomial Preconditioning with s-CG on multiprocessors with memory hierarchy.

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