# Solving symmetric-definite quadratic lambda-matrix problems without factorization

## Abstract

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented.

- Authors:

- (Univ. of Texas, Austin)

- Publication Date:

- OSTI Identifier:
- 6506875

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

- Resource Type:
- Journal Article

- Journal Name:
- SIAM J. Sci. Stat. Comput.; (United States)

- Additional Journal Information:
- Journal Volume: 3:1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HERMITIAN MATRIX; EIGENVALUES; EIGENVECTORS; ALGORITHMS; CONVERGENCE; EQUATIONS OF MOTION; GYROSCOPES; RITZ METHOD; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL LOGIC; MATRICES; PARTIAL DIFFERENTIAL EQUATIONS; 658000* - Mathematical Physics- (-1987); 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

### Citation Formats

```
Scott, D.S., and Ward, R.C.
```*Solving symmetric-definite quadratic lambda-matrix problems without factorization*. United States: N. p., 1982.
Web. doi:10.1137/0903005.

```
Scott, D.S., & Ward, R.C.
```*Solving symmetric-definite quadratic lambda-matrix problems without factorization*. United States. doi:10.1137/0903005.

```
Scott, D.S., and Ward, R.C. Mon .
"Solving symmetric-definite quadratic lambda-matrix problems without factorization". United States. doi:10.1137/0903005.
```

```
@article{osti_6506875,
```

title = {Solving symmetric-definite quadratic lambda-matrix problems without factorization},

author = {Scott, D.S. and Ward, R.C.},

abstractNote = {Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented.},

doi = {10.1137/0903005},

journal = {SIAM J. Sci. Stat. Comput.; (United States)},

number = ,

volume = 3:1,

place = {United States},

year = {1982},

month = {3}

}

DOI: 10.1137/0903005

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.