Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems

Abstract : In this paper we apply simple GMRES bounds to the nearly singular systems that arise in ill-posed problems. Our bounds depend on the eigenvalues of the coefficient matrix, the right-hand side vector and the nonnormality of the system. The bounds show that GMRES residuals initially decrease, as residual components associated with large eigenvalues are reduced, after which semi-convergence can be expected because of the effects of small eigenvalues.
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Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.230-236, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_22〉
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Jennifer Pestana. Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems. Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.230-236, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_22〉. 〈hal-01286418〉

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