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Computable error bounds and estimates for the conjugate gradient method |
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| Authors: | D. Calvetti S. Morigi L. Reichel F. Sgallari |
| Affiliation: | (1) Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA;(2) Dipartimento di Matematica, Universitá di Bologna, Bologna, Italy;(3) Department of Mathematics and Computer Science, Kent State University, Kent, OH 44242, USA;(4) Dipartimento di Matematica, Universitá di Bologna, Bologna, Italy |
| Abstract: | The 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. |
| Keywords: | Gauss quadrature rule linear system of equations Cholesky factorization |
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