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

[img] PDF

Download (167kB)
Official URL: http://epubs.siam.org/SIMAX/volume-23/art_35097.ht...


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
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

Actions (login required)

MIMS EPrints is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton. More information and software credits.