Efficient evaluation of matrix polynomials

Niv Hoffman; Oded Schwartz; Sivan Toledo

doi:10.1007/978-3-319-78024-5_3

Efficient evaluation of matrix polynomials

Niv Hoffman, Oded Schwartz, Sivan Toledo^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

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

2 Scopus citations

Abstract

We revisit the problem of evaluating matrix polynomials and introduce memory and communication efficient algorithms. Our algorithms, based on that of Patterson and Stockmeyer, are more efficient than previous ones, while being as memory-efficient as Van Loan’s variant. We supplement our theoretical analysis of the algorithms, with matching lower bounds and with experimental results showing that our algorithms outperform existing ones.

Original language	American English
Title of host publication	Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers
Editors	Jack Dongarra, Roman Wyrzykowski, Konrad Karczewski, Ewa Deelman
Publisher	Springer Verlag
Pages	24-35
Number of pages	12
ISBN (Print)	9783319780238
DOIs	https://doi.org/10.1007/978-3-319-78024-5_3
State	Published - 2018
Event	12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017 - Czestochowa, Poland Duration: 10 Sep 2017 → 13 Sep 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10777 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017
Country/Territory	Poland
City	Czestochowa
Period	10/09/17 → 13/09/17

Bibliographical note

Funding Information:
This research is supported by grants 1878/14, 1901/14, 965/15 and 863/15 from the Israel Science Foundation, grant 3-10891 from the Israeli Ministry of Science and Technology, by the Einstein and Minerva Foundations, by the PetaCloud consortium, by the Intel Collaborative Research Institute for Computational Intelligence, by a grant from the US-Israel Bi-national Science Foundation, and by the HUJI Cyber Security Research Center.

Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

Keywords

Cache efficiency
Matrix polynomials
Polynomial evaluation

Access to Document

10.1007/978-3-319-78024-5_3

Cite this

Hoffman, N., Schwartz, O., & Toledo, S. (2018). Efficient evaluation of matrix polynomials. In J. Dongarra, R. Wyrzykowski, K. Karczewski, & E. Deelman (Eds.), Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers (pp. 24-35). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10777 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-78024-5_3

Hoffman, Niv ; Schwartz, Oded ; Toledo, Sivan. / Efficient evaluation of matrix polynomials. Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. editor / Jack Dongarra ; Roman Wyrzykowski ; Konrad Karczewski ; Ewa Deelman. Springer Verlag, 2018. pp. 24-35 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{1b44d46684714ab5b2e1166a35bb9772,

title = "Efficient evaluation of matrix polynomials",

abstract = "We revisit the problem of evaluating matrix polynomials and introduce memory and communication efficient algorithms. Our algorithms, based on that of Patterson and Stockmeyer, are more efficient than previous ones, while being as memory-efficient as Van Loan{\textquoteright}s variant. We supplement our theoretical analysis of the algorithms, with matching lower bounds and with experimental results showing that our algorithms outperform existing ones.",

keywords = "Cache efficiency, Matrix polynomials, Polynomial evaluation",

author = "Niv Hoffman and Oded Schwartz and Sivan Toledo",

note = "Funding Information: This research is supported by grants 1878/14, 1901/14, 965/15 and 863/15 from the Israel Science Foundation, grant 3-10891 from the Israeli Ministry of Science and Technology, by the Einstein and Minerva Foundations, by the PetaCloud consortium, by the Intel Collaborative Research Institute for Computational Intelligence, by a grant from the US-Israel Bi-national Science Foundation, and by the HUJI Cyber Security Research Center. Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017 ; Conference date: 10-09-2017 Through 13-09-2017",

year = "2018",

doi = "10.1007/978-3-319-78024-5_3",

language = "American English",

isbn = "9783319780238",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "24--35",

editor = "Jack Dongarra and Roman Wyrzykowski and Konrad Karczewski and Ewa Deelman",

booktitle = "Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers",

address = "Germany",

}

Hoffman, N, Schwartz, O & Toledo, S 2018, Efficient evaluation of matrix polynomials. in J Dongarra, R Wyrzykowski, K Karczewski & E Deelman (eds), Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10777 LNCS, Springer Verlag, pp. 24-35, 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, Czestochowa, Poland, 10/09/17. https://doi.org/10.1007/978-3-319-78024-5_3

Efficient evaluation of matrix polynomials. / Hoffman, Niv; Schwartz, Oded; Toledo, Sivan.
Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. ed. / Jack Dongarra; Roman Wyrzykowski; Konrad Karczewski; Ewa Deelman. Springer Verlag, 2018. p. 24-35 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10777 LNCS).

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

TY - GEN

T1 - Efficient evaluation of matrix polynomials

AU - Hoffman, Niv

AU - Schwartz, Oded

AU - Toledo, Sivan

N1 - Funding Information: This research is supported by grants 1878/14, 1901/14, 965/15 and 863/15 from the Israel Science Foundation, grant 3-10891 from the Israeli Ministry of Science and Technology, by the Einstein and Minerva Foundations, by the PetaCloud consortium, by the Intel Collaborative Research Institute for Computational Intelligence, by a grant from the US-Israel Bi-national Science Foundation, and by the HUJI Cyber Security Research Center. Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - We revisit the problem of evaluating matrix polynomials and introduce memory and communication efficient algorithms. Our algorithms, based on that of Patterson and Stockmeyer, are more efficient than previous ones, while being as memory-efficient as Van Loan’s variant. We supplement our theoretical analysis of the algorithms, with matching lower bounds and with experimental results showing that our algorithms outperform existing ones.

AB - We revisit the problem of evaluating matrix polynomials and introduce memory and communication efficient algorithms. Our algorithms, based on that of Patterson and Stockmeyer, are more efficient than previous ones, while being as memory-efficient as Van Loan’s variant. We supplement our theoretical analysis of the algorithms, with matching lower bounds and with experimental results showing that our algorithms outperform existing ones.

KW - Cache efficiency

KW - Matrix polynomials

KW - Polynomial evaluation

UR - http://www.scopus.com/inward/record.url?scp=85044730698&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-78024-5_3

DO - 10.1007/978-3-319-78024-5_3

M3 - Conference contribution

AN - SCOPUS:85044730698

SN - 9783319780238

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 24

EP - 35

BT - Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers

A2 - Dongarra, Jack

A2 - Wyrzykowski, Roman

A2 - Karczewski, Konrad

A2 - Deelman, Ewa

PB - Springer Verlag

T2 - 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017

Y2 - 10 September 2017 through 13 September 2017

ER -

Hoffman N, Schwartz O, Toledo S. Efficient evaluation of matrix polynomials. In Dongarra J, Wyrzykowski R, Karczewski K, Deelman E, editors, Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. Springer Verlag. 2018. p. 24-35. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-78024-5_3

Efficient evaluation of matrix polynomials

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this