## Abstract

The short term behavior of a Markov chain can be inferred from its fundamental matrix F. One method of computing the parts of F that are needed is to compute Fy for a given vector y. It is shown that all forward stable algorithms that solve a particular least squares problem lead to forward stable algorithms for computing Fy. This in turn leads to a class of algorithms that compute Fy accurately whenever the underlying problem is well-conditioned. One algorithm from this class is based upon the Grassman-Taksar-Heyman variant of Gaussian elimination. Other such algorithms include one based upon orthogonal factorization and one based upon the conjugate gradient least squares algorithm.

Original language | English (US) |
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Pages (from-to) | 230-241 |

Number of pages | 12 |

Journal | SIAM Journal on Matrix Analysis and Applications |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2000 |

## All Science Journal Classification (ASJC) codes

- Analysis