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

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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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 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:	https://eprints.maths.manchester.ac.uk/id/eprint/319

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