### Abstract

Language | English |
---|---|

Pages | 193-214 |

Number of pages | 21 |

Journal | Linear Algebra and its Applications |

Volume | 214 |

DOIs | |

Publication status | Published - 1 Jan 1995 |

### Fingerprint

### Keywords

- normwise relative condition
- matrix inversion
- linear systems
- numerical mathematics
- vectors

### Cite this

*Linear Algebra and its Applications*,

*214*, 193-214. https://doi.org/10.1016/0024-3795(93)00066-9

}

*Linear Algebra and its Applications*, vol. 214, pp. 193-214. https://doi.org/10.1016/0024-3795(93)00066-9

**Condition numbers and their condition numbers.** / Higham, D.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Condition numbers and their condition numbers

AU - Higham, D.J.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the solution of linear systems are characterized. New results are derived for the cases where two common, noninduced matrix norms are used, and where different vector norms are used for the domain and range of the matrix. Condition numbers that respect the structure of symmetric problems are also analyzed. The sensitivity of the condition number itself is then investigated, and we obtain sharp examples of Demmel's general result that for certain problems in numerical analysis 'the condition number of the condition number is the condition number.' Finally, upper bounds are derived for the sensitivity of componentwise condition numbers.

AB - Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the solution of linear systems are characterized. New results are derived for the cases where two common, noninduced matrix norms are used, and where different vector norms are used for the domain and range of the matrix. Condition numbers that respect the structure of symmetric problems are also analyzed. The sensitivity of the condition number itself is then investigated, and we obtain sharp examples of Demmel's general result that for certain problems in numerical analysis 'the condition number of the condition number is the condition number.' Finally, upper bounds are derived for the sensitivity of componentwise condition numbers.

KW - normwise relative condition

KW - matrix inversion

KW - linear systems

KW - numerical mathematics

KW - vectors

UR - http://dx.doi.org/10.1016/0024-3795(93)00066-9

U2 - 10.1016/0024-3795(93)00066-9

DO - 10.1016/0024-3795(93)00066-9

M3 - Article

VL - 214

SP - 193

EP - 214

JO - Linear Algebra and its Applications

T2 - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -