Improved coefficients for polynomial filtering in ESSEX

Martin Galgon; Lukas Krämer; Bruno Lang; Andreas Alvermann; Holger Fehske; Andreas Pieper; Georg Hager; Moritz Kreutzer; Faisal Shahzad; Gerhard Wellein; Achim Basermann; Melven Röhrig-Zöllner; Jonas Thies

doi:10.1007/978-3-319-62426-6_5

Improved coefficients for polynomial filtering in ESSEX

Martin Galgon, Lukas Krämer, Bruno Lang^*, Andreas Alvermann, Holger Fehske, Andreas Pieper, Georg Hager, Moritz Kreutzer, Faisal Shahzad, Gerhard Wellein, Achim Basermann, Melven Röhrig-Zöllner, Jonas Thies

^*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

3 Citations (Scopus)

Abstract

The ESSEX project is an ongoing effort to provide exascale-enabled sparse eigensolvers, especially for quantum physics and related application areas. In this paper we first briefly summarize some key achievements that have been made within this project. Then we focus on a projection-based eigensolver with polynomial approximation of the projector. This eigensolver can be used for computing hundreds of interior eigenvalues of large sparse matrices. We describe techniques that allow using lower-degree polynomials than possible with standard Chebyshev expansion of the window function and kernel smoothing. With these polynomials, the degree, and thus the number of matrix–vector multiplications, typically can be reduced by roughly one half, resulting in comparable savings in runtime.

Original language	English
Title of host publication	Eigenvalue Problems
Subtitle of host publication	Algorithms, Software and Applications in Petascale Computing - EPASA 2015
Editors	Yoshinobu Kuramashi, Takeo Hoshi, Tetsuya Sakurai, Toshiyuki Imamura, Shao-Liang Zhang, Yusaku Yamamoto
Publisher	Springer
Pages	63-79
Number of pages	17
ISBN (Print)	9783319624242
DOIs	https://doi.org/10.1007/978-3-319-62426-6_5
Publication status	Published - 2017
Externally published	Yes
Event	1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 - Tsukuba, Japan Duration: 14 Sept 2015 → 16 Sept 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	117
ISSN (Print)	1439-7358

Conference

Conference	1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015
Country/Territory	Japan
City	Tsukuba
Period	14/09/15 → 16/09/15

Access to Document

10.1007/978-3-319-62426-6_5

Cite this

Galgon, M., Krämer, L., Lang, B., Alvermann, A., Fehske, H., Pieper, A., Hager, G., Kreutzer, M., Shahzad, F., Wellein, G., Basermann, A., Röhrig-Zöllner, M., & Thies, J. (2017). Improved coefficients for polynomial filtering in ESSEX. In Y. Kuramashi, T. Hoshi, T. Sakurai, T. Imamura, S.-L. Zhang, & Y. Yamamoto (Eds.), Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015 (pp. 63-79). (Lecture Notes in Computational Science and Engineering; Vol. 117). Springer. https://doi.org/10.1007/978-3-319-62426-6_5

Galgon, Martin ; Krämer, Lukas ; Lang, Bruno et al. / Improved coefficients for polynomial filtering in ESSEX. Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. editor / Yoshinobu Kuramashi ; Takeo Hoshi ; Tetsuya Sakurai ; Toshiyuki Imamura ; Shao-Liang Zhang ; Yusaku Yamamoto. Springer, 2017. pp. 63-79 (Lecture Notes in Computational Science and Engineering).

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title = "Improved coefficients for polynomial filtering in ESSEX",

abstract = "The ESSEX project is an ongoing effort to provide exascale-enabled sparse eigensolvers, especially for quantum physics and related application areas. In this paper we first briefly summarize some key achievements that have been made within this project. Then we focus on a projection-based eigensolver with polynomial approximation of the projector. This eigensolver can be used for computing hundreds of interior eigenvalues of large sparse matrices. We describe techniques that allow using lower-degree polynomials than possible with standard Chebyshev expansion of the window function and kernel smoothing. With these polynomials, the degree, and thus the number of matrix–vector multiplications, typically can be reduced by roughly one half, resulting in comparable savings in runtime.",

author = "Martin Galgon and Lukas Kr{\"a}mer and Bruno Lang and Andreas Alvermann and Holger Fehske and Andreas Pieper and Georg Hager and Moritz Kreutzer and Faisal Shahzad and Gerhard Wellein and Achim Basermann and Melven R{\"o}hrig-Z{\"o}llner and Jonas Thies",

year = "2017",

doi = "10.1007/978-3-319-62426-6_5",

language = "English",

isbn = "9783319624242",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer",

pages = "63--79",

editor = "Yoshinobu Kuramashi and Takeo Hoshi and Tetsuya Sakurai and Toshiyuki Imamura and Shao-Liang Zhang and Yusaku Yamamoto",

booktitle = "Eigenvalue Problems",

note = "1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015 ; Conference date: 14-09-2015 Through 16-09-2015",

}

Galgon, M, Krämer, L, Lang, B, Alvermann, A, Fehske, H, Pieper, A, Hager, G, Kreutzer, M, Shahzad, F, Wellein, G, Basermann, A, Röhrig-Zöllner, M & Thies, J 2017, Improved coefficients for polynomial filtering in ESSEX. in Y Kuramashi, T Hoshi, T Sakurai, T Imamura, S-L Zhang & Y Yamamoto (eds), Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Lecture Notes in Computational Science and Engineering, vol. 117, Springer, pp. 63-79, 1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015, Tsukuba, Japan, 14/09/15. https://doi.org/10.1007/978-3-319-62426-6_5

Improved coefficients for polynomial filtering in ESSEX. / Galgon, Martin; Krämer, Lukas; Lang, Bruno et al.
Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. ed. / Yoshinobu Kuramashi; Takeo Hoshi; Tetsuya Sakurai; Toshiyuki Imamura; Shao-Liang Zhang; Yusaku Yamamoto. Springer, 2017. p. 63-79 (Lecture Notes in Computational Science and Engineering; Vol. 117).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Improved coefficients for polynomial filtering in ESSEX

AU - Galgon, Martin

AU - Krämer, Lukas

AU - Lang, Bruno

AU - Alvermann, Andreas

AU - Fehske, Holger

AU - Pieper, Andreas

AU - Hager, Georg

AU - Kreutzer, Moritz

AU - Shahzad, Faisal

AU - Wellein, Gerhard

AU - Basermann, Achim

AU - Röhrig-Zöllner, Melven

AU - Thies, Jonas

PY - 2017

Y1 - 2017

N2 - The ESSEX project is an ongoing effort to provide exascale-enabled sparse eigensolvers, especially for quantum physics and related application areas. In this paper we first briefly summarize some key achievements that have been made within this project. Then we focus on a projection-based eigensolver with polynomial approximation of the projector. This eigensolver can be used for computing hundreds of interior eigenvalues of large sparse matrices. We describe techniques that allow using lower-degree polynomials than possible with standard Chebyshev expansion of the window function and kernel smoothing. With these polynomials, the degree, and thus the number of matrix–vector multiplications, typically can be reduced by roughly one half, resulting in comparable savings in runtime.

AB - The ESSEX project is an ongoing effort to provide exascale-enabled sparse eigensolvers, especially for quantum physics and related application areas. In this paper we first briefly summarize some key achievements that have been made within this project. Then we focus on a projection-based eigensolver with polynomial approximation of the projector. This eigensolver can be used for computing hundreds of interior eigenvalues of large sparse matrices. We describe techniques that allow using lower-degree polynomials than possible with standard Chebyshev expansion of the window function and kernel smoothing. With these polynomials, the degree, and thus the number of matrix–vector multiplications, typically can be reduced by roughly one half, resulting in comparable savings in runtime.

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DO - 10.1007/978-3-319-62426-6_5

M3 - Conference contribution

AN - SCOPUS:85041508487

SN - 9783319624242

T3 - Lecture Notes in Computational Science and Engineering

SP - 63

EP - 79

BT - Eigenvalue Problems

A2 - Kuramashi, Yoshinobu

A2 - Hoshi, Takeo

A2 - Sakurai, Tetsuya

A2 - Imamura, Toshiyuki

A2 - Zhang, Shao-Liang

A2 - Yamamoto, Yusaku

PB - Springer

T2 - 1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015

Y2 - 14 September 2015 through 16 September 2015

ER -

Galgon M, Krämer L, Lang B, Alvermann A, Fehske H, Pieper A et al. Improved coefficients for polynomial filtering in ESSEX. In Kuramashi Y, Hoshi T, Sakurai T, Imamura T, Zhang SL, Yamamoto Y, editors, Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing - EPASA 2015. Springer. 2017. p. 63-79. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-62426-6_5

Improved coefficients for polynomial filtering in ESSEX

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