A generalized Newton method for absolute value equations

✍ Scribed by O. L. Mangasarian

• Book ID: 107402523
• Publisher: Springer-Verlag
• Year: 2008
• Tongue: English
• Weight: 129 KB
• Volume: 3
• Category: Article
• ISSN: 1862-4472
• DOI: 10.1007/s11590-008-0094-5

✦ Synopsis

A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax -|x| = b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1,000-dimensional AVEs to an accuracy of 10 -6 in less than 10 s each. Similarly, AVEs corresponding to 100 randomly generated linear complementarity problems with 1,000 × 1,000 nonsymmetric positive definite matrices were also solved to the same accuracy in less than 29 s each.