# Solving Large-scale Eigenvalue Problems in SciDACApplications

## Abstract

Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an overview of the recent development of eigenvalue computation in the context of two SciDAC applications. We emphasize the importance of Krylov subspace methods, and point out its limitations. We discuss the value of alternative approaches that are more amenable to the use of preconditioners, and report the progression using the multi-level algebraic sub-structuring techniques to speed up eigenvalue calculation. In addition to methods for linear eigenvalue problems, we also examine new approaches to solving two types of non-linear eigenvalue problems arising from SciDAC applications.

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE Director. Office of Science. Office of AdvancedScientific Computing Research

- OSTI Identifier:
- 860916

- Report Number(s):
- LBNL-58339

R&D Project: KS1210; BnR: KJ0101010; TRN: US200603%%23

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Conference

- Resource Relation:
- Conference: SciDAC 2005, San Francisco, CA,06/26-30/2005

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; EIGENVALUES; NONLINEAR PROBLEMS; CALCULATION METHODS; eigenvalue calculation accelerator design electronic structureKrylov subspace optimization nonlinear equqation projectionmethods

### Citation Formats

```
Yang, Chao.
```*Solving Large-scale Eigenvalue Problems in SciDACApplications*. United States: N. p., 2005.
Web.

```
Yang, Chao.
```*Solving Large-scale Eigenvalue Problems in SciDACApplications*. United States.

```
Yang, Chao. Wed .
"Solving Large-scale Eigenvalue Problems in SciDACApplications". United States.
doi:. https://www.osti.gov/servlets/purl/860916.
```

```
@article{osti_860916,
```

title = {Solving Large-scale Eigenvalue Problems in SciDACApplications},

author = {Yang, Chao},

abstractNote = {Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an overview of the recent development of eigenvalue computation in the context of two SciDAC applications. We emphasize the importance of Krylov subspace methods, and point out its limitations. We discuss the value of alternative approaches that are more amenable to the use of preconditioners, and report the progression using the multi-level algebraic sub-structuring techniques to speed up eigenvalue calculation. In addition to methods for linear eigenvalue problems, we also examine new approaches to solving two types of non-linear eigenvalue problems arising from SciDAC applications.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Jun 29 00:00:00 EDT 2005},

month = {Wed Jun 29 00:00:00 EDT 2005}

}

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