You are here: MIMS > EPrints
MIMS EPrints

2006.143: Solving a quadratic matrix equation by Newton's method with exact line searches

2006.143: Nicholas J Higham and Hyun-Min Kim (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

Full text available as:

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

DOI: 10.1137/S0895479899350976

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
Uncontrolled Keywords:quadratic matrix equation, solvent, Newton's method, generalized Sylvester equation, exact line searches, quadratic eigenvalue problem, condition number, backward error
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.143
Deposited By:Miss Louise Stait
Deposited On:27 June 2006

Download Statistics: last 4 weeks
Repository Staff Only: edit this item