A blocked QR-decomposition for the parallel symmetric eigenvalue problem

T. Auckenthaler; T. Huckle; R. Wittmann

doi:10.1016/j.parco.2014.03.010

A blocked QR-decomposition for the parallel symmetric eigenvalue problem

T. Auckenthaler, T. Huckle, R. Wittmann

Informatics 5 - Chair of Scientific Computing

Technical University of Munich

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

8 Scopus citations

Abstract

In this paper we present a new stable algorithm for the parallel QR-decomposition of "tall and skinny" matrices. The algorithm has been developed for the dense symmetric eigensolver ELPA, where the QR-decomposition of tall and skinny matrices represents an important substep. Our new approach is based on the fast but unstable CholeskyQR algorithm (Stathopoulos and Wu, 2002) [1]. We show the stability of our new algorithm and provide promising results of our MPI-based implementation on a BlueGene/P and a Power6 system.

Original language	English
Pages (from-to)	186-194
Number of pages	9
Journal	Parallel Computing
Volume	40
Issue number	7
DOIs	https://doi.org/10.1016/j.parco.2014.03.010
State	Published - Jul 2014

Keywords

Eigenvalue and eigenvector computation
Parallelization
QR-decomposition
Two-step tridiagonalization

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10.1016/j.parco.2014.03.010

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AU - Wittmann, R.

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AB - In this paper we present a new stable algorithm for the parallel QR-decomposition of "tall and skinny" matrices. The algorithm has been developed for the dense symmetric eigensolver ELPA, where the QR-decomposition of tall and skinny matrices represents an important substep. Our new approach is based on the fast but unstable CholeskyQR algorithm (Stathopoulos and Wu, 2002) [1]. We show the stability of our new algorithm and provide promising results of our MPI-based implementation on a BlueGene/P and a Power6 system.

KW - Eigenvalue and eigenvector computation

KW - Parallelization

KW - QR-decomposition

KW - Two-step tridiagonalization

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VL - 40

SP - 186

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JO - Parallel Computing

JF - Parallel Computing

IS - 7

ER -

A blocked QR-decomposition for the parallel symmetric eigenvalue problem

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Keywords

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