Abstract
The goal of this paper is to make a trial for evaluating the computational efficiency of the conjugate gradient method and to discuss some practical aspects important for the user in solving large and sparse systems of linear equations arising from the discretization of boundary value problems for elliptic partial differential equations. The solution efficiency of different algorithms of the conjugate gradient method is investigated by comparison with the computational work of the solution obtained from the standard method SLOR (1-line SOR).
Comparisons are made with the same initial guess and stopping criterion in numerical experiments on test examples representative for nuclear engineering problems. Advantages in improving the rate of convergence in the SLOR method resulting from the use of compensating initial guesses are demonstrated also.
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The previous version of this paper appeared in Proc. Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado, USA, April 1992.
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Woźnicki, Z.I. On numerical analysis of conjugate gradient method. Japan J. Indust. Appl. Math. 10, 487–519 (1993). https://doi.org/10.1007/BF03167286
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DOI: https://doi.org/10.1007/BF03167286