Krylov Methods Preconditioned with Incompletely Factored Matrices on the CM-2

Berryman, Harry; Salz, Joel; Gropp, William

doi:10.21236/ada206389

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“…Often simple diagonal scaling is an adequate preconditioner and this is trivially parallellizable. For results on a Connection Machine, see Berryman, Saltz, Gropp and Mirchandaney (1989). Often this approach leads to a significant increase in iteration steps.…”

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confidence: 99%

Parallel numerical linear algebra

Demmel¹,

Heath²,

Vorst³

1993

Acta Numerica

157

109

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We s u r v ey general techniques and open problems in numerical linear algebra on parallel architectures. We rst discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing e cient algorithms. We illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem, the nonsymmetric eigenvalue problem, and the singular value decomposition. We consider dense, band and sparse matrices.

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confidence: 99%