# Solving sparse symmetric generalized eigenvalue problems without factorization

## Abstract

In this paper an iterative technique is discussed for finding the algebraic alloy smallest (or largest) eigenvalue of the generalized eigenvalue problem. A-lambda M, where A and M are real, symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A-sigma M 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.

- Authors:

- Publication Date:

- Research Org.:
- Union Carbide Corp., Oak Ridge, TN

- OSTI Identifier:
- 6151892

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

- Resource Type:
- Journal Article

- Journal Name:
- SIAM J. Numer. Anal.; (United States)

- Additional Journal Information:
- Journal Volume: 18:1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; EIGENVALUES; ANALYTICAL SOLUTION; ALGORITHMS; EIGENVECTORS; FACTORIZATION; ITERATIVE METHODS; MATHEMATICS; MATRICES; SYMMETRY; MATHEMATICAL LOGIC; 990200* - Mathematics & Computers

### Citation Formats

```
Scott, D.S.
```*Solving sparse symmetric generalized eigenvalue problems without factorization*. United States: N. p., 1981.
Web. doi:10.1137/0718008.

```
Scott, D.S.
```*Solving sparse symmetric generalized eigenvalue problems without factorization*. United States. doi:10.1137/0718008.

```
Scott, D.S. Sun .
"Solving sparse symmetric generalized eigenvalue problems without factorization". United States. doi:10.1137/0718008.
```

```
@article{osti_6151892,
```

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

author = {Scott, D.S.},

abstractNote = {In this paper an iterative technique is discussed for finding the algebraic alloy smallest (or largest) eigenvalue of the generalized eigenvalue problem. A-lambda M, where A and M are real, symmetric, and M is positive definite. It is assumed that A and M are such that it is undesirable to factor the matrix A-sigma M 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.},

doi = {10.1137/0718008},

journal = {SIAM J. Numer. Anal.; (United States)},

number = ,

volume = 18:1,

place = {United States},

year = {1981},

month = {2}

}

DOI: 10.1137/0718008

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