Higham, Nicholas J and Kim, Hyun-Min
(2001)
*Solving a quadratic matrix equation by Newton's method with exact line searches.*
SIAM Journal On Matrix Analysis And Applications, 23 (2).
pp. 303-316.
ISSN 1095-7162

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Official URL: http://epubs.siam.org/SIMAX/volume-23/art_35097.ht...

## Abstract

We show how to incorporate exact line searches into Newton's method for solving the quadratic matrix equation AX^2 + BX + C = 0, where A, B and C are square matrices. The line searches are relatively inexpensive and improve the global convergence properties of Newton's method in theory and in practice. We also derive a condition number for the problem and show how to compute the backward error of an approximate solution.

Item Type: | Article |
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Uncontrolled Keywords: | quadratic matrix equation, solvent, Newton's method, generalized Sylvester equation, exact line searches, quadratic eigenvalue problem, condition number, backward error |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 27 Jun 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/319 |

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