Parallel eigenvalue computation for banded generalized eigenvalue problems

Michael Rippl; Bruno Lang; Thomas Huckle

doi:10.1016/j.parco.2019.07.002

Parallel eigenvalue computation for banded generalized eigenvalue problems

Michael Rippl, Bruno Lang, Thomas Huckle

Informatics 5 - Chair of Scientific Computing

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider generalized eigenvalue problems Ax=Bxλ with a banded symmetric matrix A and a banded symmetric positive definite matrix B. To reduce the generalized eigenvalue problem to standard form Cy=yλ the algorithm proposed by Crawford is applied preserving the banded structure in C. We present a parallel implementation of this method for the ELPA library. Performance analysis shows the capabilities of the approach.

Original language	English
Article number	102542
Journal	Parallel Computing
Volume	88
DOIs	https://doi.org/10.1016/j.parco.2019.07.002
State	Published - Oct 2019

Keywords

Banded symmetric positive definite Generalized eigenvalue problem
Parallel implementation
Reduction to standard eigenvalue problem

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10.1016/j.parco.2019.07.002

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title = "Parallel eigenvalue computation for banded generalized eigenvalue problems",

abstract = "We consider generalized eigenvalue problems Ax=Bxλ with a banded symmetric matrix A and a banded symmetric positive definite matrix B. To reduce the generalized eigenvalue problem to standard form Cy=yλ the algorithm proposed by Crawford is applied preserving the banded structure in C. We present a parallel implementation of this method for the ELPA library. Performance analysis shows the capabilities of the approach.",

keywords = "Banded symmetric positive definite Generalized eigenvalue problem, Parallel implementation, Reduction to standard eigenvalue problem",

author = "Michael Rippl and Bruno Lang and Thomas Huckle",

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AU - Lang, Bruno

AU - Huckle, Thomas

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AB - We consider generalized eigenvalue problems Ax=Bxλ with a banded symmetric matrix A and a banded symmetric positive definite matrix B. To reduce the generalized eigenvalue problem to standard form Cy=yλ the algorithm proposed by Crawford is applied preserving the banded structure in C. We present a parallel implementation of this method for the ELPA library. Performance analysis shows the capabilities of the approach.

KW - Banded symmetric positive definite Generalized eigenvalue problem

KW - Parallel implementation

KW - Reduction to standard eigenvalue problem

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DO - 10.1016/j.parco.2019.07.002

M3 - Article

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SN - 0167-8191

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JO - Parallel Computing

JF - Parallel Computing

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Parallel eigenvalue computation for banded generalized eigenvalue problems

Abstract

Keywords

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