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A useful remark about utilization of the initial shadow residuals r^*_0 which appear in the algorithm of the BiCGSTAB(ℓ) iterative method is described. In general, the initial shadow residuals r^*_0 a...re set as same as the initial residual r^*_0 in the BiCG process. However, sometimes convergence fails, sometimes the approximate solutions degrade in view of its accuracy. Therefore we give the initial shadow residuals r^*_0 as uniform random numbers. Through some numerical experiments, it will be made clear that this remedy is effective for gaining high and stable convergence of the BiCGSTAB(ℓ) method.show more
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