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

doi:10.1016/0167-8191(89)90062-8

Parallel Computing

Volume 11, Issue 1, July 1989, Pages 37-53

https://doi.org/10.1016/0167-8191(89)90062-8 Get rights and content

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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^☆: The research was partially supported by the U.S. Department of Energy under grant DOE DEFG02-87ER25026 while the first author was at the University of Illinois.

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

Abstract

J. Comput. Appl. Math.

Lin. Alg. Appl.

Parallel Comput.

m-Step preconditioned conjugate gradient methods

SIAM J. Sci. Statist. Comput.

A modified conjugate gradient solver for very large systems

Block preconditioning for the conjugate gradient method

SIAM J. Sci. Statist. Comput.

A class of parallel iterative methods implemented on multiprocessors

Linear algebra on high-performance computers

Approximating the inverse of a matrix for use in iterative algorithms on vector processors

Computing