## Abstract

We present two new algorithms for investigating the stability of large and sparse matrices subject to real perturbations. The first algorithm computes the real structured pseudospectral abscissa and is based on the algorithm for computing the pseudospectral abscissa proposed by Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166-1192]. It entails finding the rightmost eigenvalues for a sequence of large matrices, and we demonstrate that these eigenvalue problems can be solved in a robust manner by an unconventional eigenvalue solver. We also develop an algorithm for computing the real stability radius of a real and stable matrix, which utilizes a recently developed technique for detecting the loss of stability in a large dynamical system. Both algorithms are tested on large and sparse matrices.

Original language | English (US) |
---|---|

Pages (from-to) | S447-S471 |

Journal | SIAM Journal on Scientific Computing |

Volume | 37 |

Issue number | 5 |

DOIs | |

State | Published - 2015 |

Externally published | Yes |

## Keywords

- Abscissa
- Eigenvalue
- Lyapunov equation
- Real structured pseudospectrum
- Sparse matrix
- Stability radius

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics