## Abstract

This paper discusses techniques for computing a few selected eigenvalue–eigenvector pairs of large and sparse symmetric matrices. A recently developed class of techniques to solve this type of problems is based on integrating the matrix resolvent operator along a complex contour that encloses the interval containing the eigenvalues of interest. This paper considers such contour integration techniques from a domain decomposition viewpoint and proposes two schemes. The first scheme can be seen as an extension of domain decomposition linear system solvers in the framework of contour integration methods for eigenvalue problems, such as FEAST. The second scheme focuses on integrating the resolvent operator primarily along the interface region defined by adjacent subdomains. A parallel implementation of the proposed schemes is described, and results on distributed computing environments are reported. These results show that domain decomposition approaches can lead to reduced run times and improved scalability.

Original language | English (US) |
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Article number | e2154 |

Journal | Numerical Linear Algebra with Applications |

Volume | 25 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2018 |

### Bibliographical note

Funding Information:This work was supported jointly by NSF under awards CCF-1505970 and CCF-1510010, and by the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences under award number DE-SC0008877. Vassilis Kalantzis was also partially supported by a Gerondelis Foundation Fellowship.

Funding Information:

NSF, Grant/Award Number: CCF-1505970 and CCF-1510010; Advanced Computing (SciDAC); U.S. Department of Energy; Office of Science; Advanced Scientific Computing Research; Basic Energy Sciences, Grant/Award Number: DE-SC0008877; Gerondelis Foundation Fellowship

## Keywords

- Cauchy integral formula
- FEAST
- domain decomposition
- parallel computing
- symmetric eigenvalue problem