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

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    Type
    Book Chapter
    Authors
    Pestana, Jennifer
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2014-11-28
    Online Publication Date
    2014-11-28
    Print Publication Date
    2014
    Permanent link to this record
    http://hdl.handle.net/10754/599513
    
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    Abstract
    © IFIP International Federation for Information Processing 2014. 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.
    Citation
    Pestana J (2014) Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems. System Modeling and Optimization: 230–236. Available: http://dx.doi.org/10.1007/978-3-662-45504-3_22.
    Sponsors
    This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Springer Nature
    Journal
    IFIP Advances in Information and Communication Technology
    DOI
    10.1007/978-3-662-45504-3_22
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-662-45504-3_22
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