Abstract

The GMRES(m) method is one of the most popular iterative method for the solution of large linear systems Ax = b with nonsymmetric and sparse coefficient matrix.

Shifted linear systems A'x' = b, (A' = A + cI) are generally used in lattice gauge computations in quantum chromodynamics (see Wilson[3]). Since the Krylov subspace for the shifted linear system is equal to the original one, the Shifted-GMRES(m) method, which is proposed by A. Frommer et al.[1], can be used. This method can be reduced the matrix-vector products and the computation time. In this talk, we compare this method with the several GMRES(m) like methods and show the effectiveness by using the numerical experiments on the parallel machine Origin 2000.

REFERENCES

[1] Frommer, A. and Glassner, U.: Restarted GMRES for shifted linear systems, SIAM J. Sci. Comput., Vol. 19, No. 1, pp. 15-26 (1998).

[2] Saad, Y. and Schultz, M. H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., Vol. 7, pp. 856-869 (1986).

[3] Wilson, K. : Quarks and strings on a lattice, in New Phenomena in Subnuclear Physics, Zichichi, A. ed., Plenum, New York, pp. 69-142 (1975).

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