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

^*Bu çalışma için yazışmadan sorumlu yazar

Istanbul Technical University

Araştırma çıktısı: Kitap/Rapor/Konferans Bildirisinde Bölüm › Konferans katkısı › Hakem

Özet

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.

Orijinal dil	İngilizce
Ana bilgisayar yayını başlığı	Advances in Applied Mathematics
Editörler	Ali R. Ansari
Yayınlayan	Springer New York LLC
Sayfalar	153-160
Sayfa sayısı	8
ISBN (Elektronik)	9783319069227
DOI'lar	https://doi.org/10.1007/978-3-319-06923-4_14
Yayın durumu	Yayınlandı - 2014
Etkinlik	Gulf International Conference on Applied Mathematics, GICAM 2013 - Kuwait, Kuwait Süre: 19 Kas 2013 → 21 Kas 2013

Yayın serisi

Adı	Springer Proceedings in Mathematics and Statistics
Hacim	87
ISSN (Basılı)	2194-1009
ISSN (Elektronik)	2194-1017

???event.eventtypes.event.conference???

???event.eventtypes.event.conference???	Gulf International Conference on Applied Mathematics, GICAM 2013
Ülke/Bölge	Kuwait
Şehir	Kuwait
Periyot	19/11/13 → 21/11/13

Bibliyografik not

Publisher Copyright:
© Springer International Publishing Switzerland 2014.

Finansman

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.

Finansörler	Finansör numarası
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

Belgeye Erişim

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

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

@inproceedings{909034d85c6644ed8d5307e9ddb625e9,

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",

}

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, hac. 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; Hac. 87).

Araştırma çıktısı: Kitap/Rapor/Konferans Bildirisinde Bölüm › Konferans katkısı › Hakem

TY - GEN

T1 - Spectral analysis of large sparse matrices for scalable direct solvers

AU - Duran, Ahmet

AU - Celebi, M. Serdar

AU - Tuncel, Mehmet

AU - Oztoprak, Figen

PY - 2014

Y1 - 2014

N2 - 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.

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.

KW - Defective matrices

KW - Sparse solver

KW - Spectral analysis

UR - https://www.scopus.com/pages/publications/84927588199

U2 - 10.1007/978-3-319-06923-4_14

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

M3 - Conference contribution

AN - SCOPUS:84927588199

T3 - Springer Proceedings in Mathematics and Statistics

SP - 153

EP - 160

BT - Advances in Applied Mathematics

A2 - Ansari, Ali R.

PB - Springer New York LLC

T2 - Gulf International Conference on Applied Mathematics, GICAM 2013

Y2 - 19 November 2013 through 21 November 2013

ER -

Spectral analysis of large sparse matrices for scalable direct solvers

Özet

Yayın serisi

???event.eventtypes.event.conference???

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap