On the Behavior of the Residual in Conjugate Gradient Method
For numerical linear algebra researchers, this provides a refined understanding of residual behavior in finite precision, but it is an incremental analysis of a known phenomenon.
The paper analyzes the difference between recursively computed and true residuals in the conjugate gradient method under finite arithmetic, focusing on lower bounds caused by loss of trailing digits.
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 be-havior 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.