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Computable error bounds and estimates for the conjugate gradient method

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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.

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Calvetti, D., Morigi, S., Reichel, L. et al. Computable error bounds and estimates for the conjugate gradient method. Numerical Algorithms 25, 75–88 (2000). https://doi.org/10.1023/A:1016661024093

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  • DOI: https://doi.org/10.1023/A:1016661024093

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