Direct methods for solving singular nonlinear equations

Authors
Allgower, EL Bohmer, K Hoy, A Janovsky, V
Citation
El. Allgower et al., Direct methods for solving singular nonlinear equations, Z ANG MA ME, 79(4), 1999, pp. 219-231
Citations number
32
Categorie Soggetti
Mechanical Engineering
Journal title
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
ISSN journal
00442267 → ACNP
Volume
79
Issue
4
Year of publication
1999
Pages
219 - 231
Database
ISI
SICI code
0044-2267(1999)79:4<219:DMFSSN>2.0.ZU;2-#
Abstract
A class of Newton-type methods for computing singular points with corank gr eater than or equal to 1 and index greater than or equal to 0 is presented. The idea is to use a generalized Sherman-Morrison formula to define a regu larizing perturbation of the Newton-increment formula. The quadratic conver gence of the process is preserved. The proposed approach may be linked to t ensor methods, bordered Jacobian techniques, and numerical Liapunov-Schmidt reduction.