# Solving quadratic lambda-matrix problems without factorization

## Abstract

An algorithm is presented for computing the eigenvalues of smallest magnitude and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ + C lambda + K. M, C, and K are assumed to be symmetric matrices with K positive definite and M negative definite. The algorithm is based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence to the smallest positive and negative eigenvalue is proved. Test examples are presented.

- Authors:

- Publication Date:

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

- OSTI Identifier:
- 6654481

- Alternate Identifier(s):
- OSTI ID: 6654481

- Report Number(s):
- ORNL/CSD-76

- 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; EIGENVECTORS; MATRICES; MATHEMATICAL LOGIC 990200* -- Mathematics & Computers

### Citation Formats

```
Scott, D.S., and Ward, R.C.
```*Solving quadratic lambda-matrix problems without factorization*. United States: N. p., 1981.
Web.

```
Scott, D.S., & Ward, R.C.
```*Solving quadratic lambda-matrix problems without factorization*. United States.

```
Scott, D.S., and Ward, R.C. Sun .
"Solving quadratic lambda-matrix problems without factorization". United States.
```

```
@article{osti_6654481,
```

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

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

abstractNote = {An algorithm is presented for computing the eigenvalues of smallest magnitude and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ + C lambda + K. M, C, and K are assumed to be symmetric matrices with K positive definite and M negative definite. The algorithm is based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence to the smallest positive and negative eigenvalue is proved. Test examples are presented.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1981},

month = {3}

}

Other availability

Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that may hold this item. Keep in mind that many technical reports are not cataloged in WorldCat.

Save to My Library

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