### Abstract

The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, 2013). Here we present an new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute (Formula presented.) eigenvalues of the generalized symmetric eigenvalue problem in (Formula presented.) operations, where (Formula presented.) is a small constant.

Original language | English |
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Journal | Computing and Visualization in Science |

DOIs | |

Publication status | Accepted/In press - Mar 4 2015 |

Externally published | Yes |

### Fingerprint

### Keywords

- $${\fancyscript{H}}^2$$H2-matrices
- Slicing the spectrum
- Symmetric generalized eigenproblem

### ASJC Scopus subject areas

- Modelling and Simulation
- Theoretical Computer Science
- Software
- Computer Vision and Pattern Recognition
- Computational Theory and Mathematics
- Engineering(all)

### Cite this

*Computing and Visualization in Science*. https://doi.org/10.1007/s00791-015-0238-y

**Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum.** / Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut.

Research output: Contribution to journal › Article

*Computing and Visualization in Science*. https://doi.org/10.1007/s00791-015-0238-y

}

TY - JOUR

T1 - Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum

AU - Benner, Peter

AU - Börm, Steffen

AU - Mach, Thomas

AU - Reimer, Knut

PY - 2015/3/4

Y1 - 2015/3/4

N2 - The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, 2013). Here we present an new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute (Formula presented.) eigenvalues of the generalized symmetric eigenvalue problem in (Formula presented.) operations, where (Formula presented.) is a small constant.

AB - The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol 56. Mathematisches Forschungsinstitut, Oberwolfach, 2013). Here we present an new algorithm based on slicing the spectrum that takes advantage of the rank structure of resolvent matrices in order to compute (Formula presented.) eigenvalues of the generalized symmetric eigenvalue problem in (Formula presented.) operations, where (Formula presented.) is a small constant.

KW - $${\fancyscript{H}}^2$$H2-matrices

KW - Slicing the spectrum

KW - Symmetric generalized eigenproblem

UR - http://www.scopus.com/inward/record.url?scp=84923888517&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923888517&partnerID=8YFLogxK

U2 - 10.1007/s00791-015-0238-y

DO - 10.1007/s00791-015-0238-y

M3 - Article

JO - Computing and Visualization in Science

JF - Computing and Visualization in Science

SN - 1432-9360

ER -