Matrices, Moments and Quadrature Ii or How to Compute the Norm of the Error in Iterative Methods
نویسنده
چکیده
Abstract. In this paper, we study the numerical computation of the errors in linear systems when using iterative methods. This is done by using methods to obtain bounds or approximations of quadratic forms uT A−1u where A is a symmetric positive definite matrix and u is a given vector. Numerical examples are given for the Gauss–Seidel algorithm. Moreover, we show that using a formula for the A–norm of the error from [2], very good bounds of the error can be computed almost for free during the iterations of the conjugate gradient method leading to a reliable stopping criteria.
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تاریخ انتشار 1996