# Robust incremental condition estimation

## Abstract

This paper presents an improved version of incremental condition estimation, a technique for tracking the extremal singular values of a triangular matrix as it is being constructed one column at a time. We present a new motivation for this estimation technique using orthogonal projections. The paper focuses on an implementation of this estimation scheme in an accurate and consistent fashion. In particular, we address the subtle numerical issues arising in the computation of the eigensystem of a symmetric rank-one perturbed diagonal 2 {times} 2 matrix. Experimental results show that the resulting scheme does a good job in estimating the extremal singular values of triangular matrices, independent of matrix size and matrix condition number, and that it performs qualitatively in the same fashion as some of the commonly used nonincremental condition estimation schemes.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab., IL (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 10133022

- Report Number(s):
- ANL/MCS/PP-73012

ON: DE94008128

- DOE Contract Number:
- W-31109-ENG-38

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 29 Mar 1991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MATRICES; SINGULARITY; FACTORIZATION; ALGORITHMS; EIGENVALUES; 990200; MATHEMATICS AND COMPUTERS

### Citation Formats

```
Bischof, C.H., and Tang, P.T.P..
```*Robust incremental condition estimation*. United States: N. p., 1991.
Web. doi:10.2172/10133022.

```
Bischof, C.H., & Tang, P.T.P..
```*Robust incremental condition estimation*. United States. doi:10.2172/10133022.

```
Bischof, C.H., and Tang, P.T.P.. Fri .
"Robust incremental condition estimation". United States. doi:10.2172/10133022. https://www.osti.gov/servlets/purl/10133022.
```

```
@article{osti_10133022,
```

title = {Robust incremental condition estimation},

author = {Bischof, C.H. and Tang, P.T.P.},

abstractNote = {This paper presents an improved version of incremental condition estimation, a technique for tracking the extremal singular values of a triangular matrix as it is being constructed one column at a time. We present a new motivation for this estimation technique using orthogonal projections. The paper focuses on an implementation of this estimation scheme in an accurate and consistent fashion. In particular, we address the subtle numerical issues arising in the computation of the eigensystem of a symmetric rank-one perturbed diagonal 2 {times} 2 matrix. Experimental results show that the resulting scheme does a good job in estimating the extremal singular values of triangular matrices, independent of matrix size and matrix condition number, and that it performs qualitatively in the same fashion as some of the commonly used nonincremental condition estimation schemes.},

doi = {10.2172/10133022},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Mar 29 00:00:00 EST 1991},

month = {Fri Mar 29 00:00:00 EST 1991}

}