# Solving sparse symmetric generalized eigenvalue problems without factorization

## Abstract

An iterative technique is discussed for finding the algebraically smallest (or largest) eigenvalue of the generalized eigenvalue problem A - lambdaM, where A and M are real and symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A - sigmaM for any value of sigma. It is proved that the algorithm is globally convergent and that convergence is asymptotically quadratic. Finally, the modifications required in the algorithm to make it computationally feasible are discussed. 7 tables.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab., TN (USA)

- OSTI Identifier:
- 5879482

- Report Number(s):
- ORNL/CSD-49

- DOE Contract Number:
- W-7405-ENG-26

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; EIGENVALUES; CALCULATION METHODS; MATRICES; ITERATIVE METHODS; SERIES EXPANSION; MATHEMATICAL LOGIC; 990200* - Mathematics & Computers

### Citation Formats

```
Scott, D.S.
```*Solving sparse symmetric generalized eigenvalue problems without factorization*. United States: N. p., 1979.
Web.

```
Scott, D.S.
```*Solving sparse symmetric generalized eigenvalue problems without factorization*. United States.

```
Scott, D.S. Mon .
"Solving sparse symmetric generalized eigenvalue problems without factorization". United States.
```

```
@article{osti_5879482,
```

title = {Solving sparse symmetric generalized eigenvalue problems without factorization},

author = {Scott, D.S.},

abstractNote = {An iterative technique is discussed for finding the algebraically smallest (or largest) eigenvalue of the generalized eigenvalue problem A - lambdaM, where A and M are real and symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A - sigmaM for any value of sigma. It is proved that the algorithm is globally convergent and that convergence is asymptotically quadratic. Finally, the modifications required in the algorithm to make it computationally feasible are discussed. 7 tables.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1979},

month = {10}

}

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