This title appears in the Scientific Report :
2014
Please use the identifier:
http://dx.doi.org/10.1007/978-3-642-55224-3_3 in citations.
Performance of Dense Eigensolvers on BlueGene/Q
Performance of Dense Eigensolvers on BlueGene/Q
Many scientific applications require the computation of about 10–30 % of the eigenvalues and eigenvectors of large dense symmetric or complex hermitian matrices. In this paper we will present performance evaluation results of the eigensolvers of the three libraries Elemental, ELPA, and ScaLAPACK on...
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Personal Name(s): | Gutheil, Inge (Corresponding Author) |
---|---|
Münchhalfen, Jan Felix / Grotendorst, Johannes | |
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Published in: |
Parallel Processing and Applied Mathematics |
Imprint: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2014
|
Physical Description: |
26 - 35 |
ISBN: |
978-3-642-55224-3 (electronic) 978-3-642-55223-6 (print) |
DOI: |
10.1007/978-3-642-55224-3_3 |
Conference: | Parallel Processing and Applied Mathematics 2013, Warschau (Polen), 2013-09-08 - 2013-09-11 |
Document Type: |
Contribution to a book Contribution to a conference proceedings |
Research Program: |
Computational Science and Mathematical Methods |
Series Title: |
Lecture Notes in Computer Science
8384 |
Publikationsportal JuSER |
Many scientific applications require the computation of about 10–30 % of the eigenvalues and eigenvectors of large dense symmetric or complex hermitian matrices. In this paper we will present performance evaluation results of the eigensolvers of the three libraries Elemental, ELPA, and ScaLAPACK on the BlueGene/Q architecture. All libraries include solvers for the computation of only a part of the spectrum. The most time-consuming part of the eigensolver is the reduction of the full eigenproblem to a tridiagonal one. Whereas Elemental and ScaLAPACK only offer routines to directly reduce the full matrix to a tridiagonal one, which only allows the use of BLAS 2 matrix-vector operations and needs a lot of communication, ELPA also offers a two-step reduction routine, first transforming the full matrix to banded form and thereafter to tridiagonal form. This two-step reduction shortens the reduction time significantly but at the cost of a higher complexity of the back transformation step. We will show up to which part of the eigenspectrum the use of the two-step reduction pays off. |