On the Behavior of the Residual in Conjugate Gradient Method

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.Comment: 8 page

Computable error bounds and estimates for the conjugate gradient method

none4siThe conjugate gradient method is one of the most popular iterative methods for computing approximate solutions of linear systems of equations with a symmetric positive definite matrix A. It is generally desirable to terminate the iterations as soon as a sufficiently accurate approximate solution has been computed. This paper discusses known and new methods for computing bounds or estimates of the A-norm of the error in the approximate solutions generated by the conjugate gradient method.noneCalvetti D.; Morigi S.; Reichel L.; Sgallari F.Calvetti D.; Morigi S.; Reichel L.; Sgallari F