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

Jennifer Pestana

doi:10.1007/978-3-662-45504-3_22

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

Jennifer Pestana

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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.

Original language	English (US)
Title of host publication	IFIP Advances in Information and Communication Technology
Publisher	Springer Nature
Pages	230-236
Number of pages	7
ISBN (Print)	9783662455036
DOIs	https://doi.org/10.1007/978-3-662-45504-3_22
State	Published - Nov 28 2014
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1007/978-3-662-45504-3_22

Cite this

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abstract = "{\textcopyright} 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.",

author = "Jennifer Pestana",

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doi = "10.1007/978-3-662-45504-3_22",

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N2 - © 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.

AB - © 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.

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M3 - Chapter

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SP - 230

EP - 236

BT - IFIP Advances in Information and Communication Technology

PB - Springer Nature

ER -

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

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