## 2006.140: Numerical analysis of a quadratic matrix equation

2006.140:
Nicholas J Higham and Hyun-Min Kim
(2000)
*Numerical analysis of a quadratic matrix equation.*
IMA Journal of Numerical Analysis, 20.
pp. 499-519.
ISSN 1464-3642

Full text available as:

PDF - Archive staff only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 164 Kb |

## Abstract

The quadratic matrix equation AX2+ BX + C = 0in n x nmatrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration methods based on Bernoulli’s method. Other methods considered include Newton’s method with exact line searches, symbolic solution and continued fractions. We show that functional iteration applied to the quadratic matrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem ({lambda}2A + {lambda}B + C)x = 0.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | quadratic matrix equation; solvent; generalized Schur decomposition; scaling; functional iteration; Bernoulli’s method; Newton’s method; exact line searches; continued fractions; quadratic eigenvalue problem |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.140 |

Deposited By: | Miss Louise Stait |

Deposited On: | 27 June 2006 |

Download Statistics: last 4 weeks

Repository Staff Only: edit this item