On error estimation in the conjugate gradient method: Normwise backward error

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Petr Tichý

Abstract

Using an idea of Duff and V{\"o}mel [BIT, 42 (2002), pp.~300--322 ] we suggest a simple algorithm that incrementally estimates the $2$-norm of Jacobi matrices that are available during the conjugate gradient (CG) computations. The estimate can be used, e.g., in stopping criteria based on the normwise backward error. Numerical experiments predict  that the estimate approximates the $2$-norm of $A$ with a sufficient accuracy.

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How to Cite
TICHÝ, Petr. On error estimation in the conjugate gradient method: Normwise backward error. Proceedings of the Conference Algoritmy, [S.l.], p. 323-332, feb. 2016. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/421>. Date accessed: 22 sep. 2017.
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