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Comparison of several iterative techniques in the solution of symmetric banded equations on a two-pipe Cyber 205. (English) Zbl 0692.65010

The numerical solution of partial differential equations (five model problems are described) is often led to the solution of a matrix equation. The effectiveness of several iterative techniques for solving these matrix equations are compared.
The techniques are: the strongly implicit procedure of H. L. Stone [SIAM J. Numer. Anal. 5, 530-558 (1968; Zbl 0197.133)]; the incomplete Cholesky conjugate-gradient method, including its vectorized and also a polynomial variant and the modified form of I. Gustafsson [BIT 18, 142-156 (1978; Zbl 0386.65006)]; a diagonally scaled conjugate-gradient method and the polynomial preconditioned conjugate-gradient method of Y. Saad [SIAM J. Sci. Stat. Comput. 6, 865-881 (1985; Zbl 0601.65019)].
The comparisons are made on a vector machine. Results of the tests are presented in two tables (timing, iteration parameters, iteration counts and the megaflop rate for the iteration loop of each algorithm).
Reviewer: H.-J.Sprengel

MSC:

65F10 Iterative numerical methods for linear systems
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References:

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