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

@inproceedings{Pestana2013RightHandSD, title={Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems}, author={Jennifer Pestana}, booktitle={System Modelling and Optimization}, year={2013} }

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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