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On the Behavior of the Residual in Conjugate Gradient Method
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Applied Mathematics·Volume 01 (2010)·Pages 211–214·Published 29 September 2010·DOI10.4236/am.2010.13025
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Abstract
In conjugate gradient method, it is well known that the recursively computed residual differs from true one as the iteration proceeds in finite arithmetic. Some work have been devoted to analyze this behavior and to evaluate the lower and the upper bounds of the difference. This paper focuses on the behavior of these two kinds of residuals, especially their lower bounds caused by the loss of trailing digit, respectively.
KeywordsConjugate GradientResidualConvergenceFinite ArithmeticLower Bound
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