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

Mathematics And Statistics

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

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.

Original language	English
Title of host publication	System Modeling and Optimization
Subtitle of host publication	26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers
Editors	Christian Pötzsche, Clemens Heuberger, Barbara Kaltenbacher, Franz Rendl
Place of Publication	Heidelberg
Publisher	Springer-Verlag
Pages	230-236
Number of pages	7
ISBN (Print)	9783662455036
DOIs	https://doi.org/10.1007/978-3-662-45504-3_22
Publication status	Published - 28 Nov 2014
Event	26th IFIP TC 7 Conference on System Modeling and Optimization - Klagenfurt, Austria Duration: 8 Sep 2013 → 13 Sep 2013

Publication series

Name	IFIP Advances in Information and Communication Technology
Publisher	Springer-Verlag
Volume	443
ISSN (Print)	1868-4238

Conference

Conference	26th IFIP TC 7 Conference on System Modeling and Optimization
Country/Territory	Austria
City	Klagenfurt
Period	8/09/13 → 13/09/13

Keywords

GMRES
convergence
ill-posed problem
eigenvalues
generalized minimal residual method

Access to Document

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

Cite this

Pestana, J. (2014). Right-hand side dependent bounds for GMRES applied to ill-posed problems. In C. Pötzsche, C. Heuberger, B. Kaltenbacher, & F. Rendl (Eds.), System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers (pp. 230-236). (IFIP Advances in Information and Communication Technology; Vol. 443). Springer-Verlag. https://doi.org/10.1007/978-3-662-45504-3_22

Pestana, Jennifer. / Right-hand side dependent bounds for GMRES applied to ill-posed problems. System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. editor / Christian Pötzsche ; Clemens Heuberger ; Barbara Kaltenbacher ; Franz Rendl. Heidelberg : Springer-Verlag, 2014. pp. 230-236 (IFIP Advances in Information and Communication Technology).

@inproceedings{7c76e107528d4d75940ccf6512182471,

title = "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.",

keywords = "GMRES, convergence, ill-posed problem, eigenvalues, generalized minimal residual method",

author = "Jennifer Pestana",

year = "2014",

month = nov,

day = "28",

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

language = "English",

isbn = "9783662455036",

series = "IFIP Advances in Information and Communication Technology",

publisher = "Springer-Verlag",

pages = "230--236",

editor = "Christian P{\"o}tzsche and Clemens Heuberger and Barbara Kaltenbacher and Franz Rendl",

booktitle = "System Modeling and Optimization",

note = "26th IFIP TC 7 Conference on System Modeling and Optimization ; Conference date: 08-09-2013 Through 13-09-2013",

}

Pestana, J 2014, Right-hand side dependent bounds for GMRES applied to ill-posed problems. in C Pötzsche, C Heuberger, B Kaltenbacher & F Rendl (eds), System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. IFIP Advances in Information and Communication Technology, vol. 443, Springer-Verlag, Heidelberg, pp. 230-236, 26th IFIP TC 7 Conference on System Modeling and Optimization, Klagenfurt, Austria, 8/09/13. https://doi.org/10.1007/978-3-662-45504-3_22

Right-hand side dependent bounds for GMRES applied to ill-posed problems. / Pestana, Jennifer.

System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. ed. / Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. Heidelberg : Springer-Verlag, 2014. p. 230-236 (IFIP Advances in Information and Communication Technology; Vol. 443).

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

TY - GEN

T1 - Right-hand side dependent bounds for GMRES applied to ill-posed problems

AU - Pestana, Jennifer

PY - 2014/11/28

Y1 - 2014/11/28

N2 - 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 - 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.

KW - GMRES

KW - convergence

KW - ill-posed problem

KW - eigenvalues

KW - generalized minimal residual method

UR - http://link.springer.com/book/10.1007/978-3-662-45504-3

U2 - 10.1007/978-3-662-45504-3_22

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

M3 - Conference contribution book

SN - 9783662455036

T3 - IFIP Advances in Information and Communication Technology

SP - 230

EP - 236

BT - System Modeling and Optimization

A2 - Pötzsche, Christian

A2 - Heuberger, Clemens

A2 - Kaltenbacher, Barbara

A2 - Rendl, Franz

PB - Springer-Verlag

CY - Heidelberg

T2 - 26th IFIP TC 7 Conference on System Modeling and Optimization

Y2 - 8 September 2013 through 13 September 2013

ER -

Pestana J. Right-hand side dependent bounds for GMRES applied to ill-posed problems. In Pötzsche C, Heuberger C, Kaltenbacher B, Rendl F, editors, System Modeling and Optimization: 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9-13, 2013, Revised Selected Papers. Heidelberg: Springer-Verlag. 2014. p. 230-236. (IFIP Advances in Information and Communication Technology). https://doi.org/10.1007/978-3-662-45504-3_22

Right-hand side dependent bounds for GMRES applied to ill-posed problems

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Cite this