Spectral analysis of large sparse matrices for scalable direct solvers

Ahmet Duran; M. Serdar Celebi; Mehmet Tuncel; Figen Oztoprak

doi:10.1007/978-3-319-06923-4_14

Spectral analysis of large sparse matrices for scalable direct solvers

Ahmet Duran^*, M. Serdar Celebi, Mehmet Tuncel, Figen Oztoprak

^*Corresponding author for this work

Istanbul Technical University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

It is significant to perform structural analysis of large sparse matrices in order to obtain scalable direct solvers. In this paper, we focus on spectral analysis of large sparse matrices. We believe that the approach for exception handling of challenging matrices via Gerschgorin circles and using tuned parameters is beneficial and practical to stabilize the performance of sparse direct solvers. Nearly defective matrices are among challenging matrices for the performance of solver. Such matrices should be handled separately in order to get rid of potential performance bottleneck. Clustered eigenvalues observed via Gerschgorin circles may be used to detect nearly defective matrix. We observe that the usage of super-nodal storage parameters affects the number of fill-ins and memory usage accordingly.

Original language	English
Title of host publication	Advances in Applied Mathematics
Editors	Ali R. Ansari
Publisher	Springer New York LLC
Pages	153-160
Number of pages	8
ISBN (Electronic)	9783319069227
DOIs	https://doi.org/10.1007/978-3-319-06923-4_14
Publication status	Published - 2014
Event	Gulf International Conference on Applied Mathematics, GICAM 2013 - Kuwait, Kuwait Duration: 19 Nov 2013 → 21 Nov 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	87
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Gulf International Conference on Applied Mathematics, GICAM 2013
Country/Territory	Kuwait
City	Kuwait
Period	19/11/13 → 21/11/13

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2014.

Funding

This work was financially supported by the PRACE project funded in part by the EUs 7th Framework Programme (FP7/2011–2013) under grant agreement no. RI-283493. Computing resources used in this work were provided by the National Center for High Performance Computing of Turkey (UHeM) (see []) under grant number 1001682012.

Funders	Funder number
National Center for High Performance Computing of Turkey	1001682012
Partnership for Advanced Computing in Europe AISBL
Seventh Framework Programme	RI-283493
Partnership for Advanced Computing in Europe AISBL

Keywords

Defective matrices
Sparse solver
Spectral analysis

Access to Document

10.1007/978-3-319-06923-4_14

Cite this

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title = "Spectral analysis of large sparse matrices for scalable direct solvers",

abstract = "It is significant to perform structural analysis of large sparse matrices in order to obtain scalable direct solvers. In this paper, we focus on spectral analysis of large sparse matrices. We believe that the approach for exception handling of challenging matrices via Gerschgorin circles and using tuned parameters is beneficial and practical to stabilize the performance of sparse direct solvers. Nearly defective matrices are among challenging matrices for the performance of solver. Such matrices should be handled separately in order to get rid of potential performance bottleneck. Clustered eigenvalues observed via Gerschgorin circles may be used to detect nearly defective matrix. We observe that the usage of super-nodal storage parameters affects the number of fill-ins and memory usage accordingly.",

keywords = "Defective matrices, Sparse solver, Spectral analysis",

author = "Ahmet Duran and Celebi, {M. Serdar} and Mehmet Tuncel and Figen Oztoprak",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.; Gulf International Conference on Applied Mathematics, GICAM 2013 ; Conference date: 19-11-2013 Through 21-11-2013",

year = "2014",

doi = "10.1007/978-3-319-06923-4_14",

language = "English",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "153--160",

editor = "Ansari, {Ali R.}",

booktitle = "Advances in Applied Mathematics",

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Duran, A , Celebi, MS , Tuncel, M & Oztoprak, F 2014, Spectral analysis of large sparse matrices for scalable direct solvers. in AR Ansari (ed.), Advances in Applied Mathematics. Springer Proceedings in Mathematics and Statistics, vol. 87, Springer New York LLC, pp. 153-160, Gulf International Conference on Applied Mathematics, GICAM 2013, Kuwait, Kuwait, 19/11/13. https://doi.org/10.1007/978-3-319-06923-4_14

Spectral analysis of large sparse matrices for scalable direct solvers. / Duran, Ahmet ; Celebi, M. Serdar ; Tuncel, Mehmet et al.
Advances in Applied Mathematics. ed. / Ali R. Ansari. Springer New York LLC, 2014. p. 153-160 (Springer Proceedings in Mathematics and Statistics; Vol. 87).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Tuncel, Mehmet

AU - Oztoprak, Figen

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AB - It is significant to perform structural analysis of large sparse matrices in order to obtain scalable direct solvers. In this paper, we focus on spectral analysis of large sparse matrices. We believe that the approach for exception handling of challenging matrices via Gerschgorin circles and using tuned parameters is beneficial and practical to stabilize the performance of sparse direct solvers. Nearly defective matrices are among challenging matrices for the performance of solver. Such matrices should be handled separately in order to get rid of potential performance bottleneck. Clustered eigenvalues observed via Gerschgorin circles may be used to detect nearly defective matrix. We observe that the usage of super-nodal storage parameters affects the number of fill-ins and memory usage accordingly.

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Spectral analysis of large sparse matrices for scalable direct solvers

Abstract

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Conference

Bibliographical note

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Keywords

Access to Document

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