| Texto completo | |
| Autor(es): |
Martinez, Jose Mario
;
Santos, Lucio Tunes
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | NUMERICAL ALGORITHMS; v. N/A, p. 19-pg., 2022-04-06. |
| Resumo | |
Quasi-Newton methods for solving nonlinear systems of equations are generally defined in order to satisfy a "direct secant equation" or an "inverse secant equation" at every iteration. The classical Dennis-More condition, which, under suitable local assumptions, implies superlinear convergence, is related to the direct secant equation. A natural modification of the Dennis-More condition that evokes the inverse secant equation will be considered and two conjectures related to convergence will be formulated. In spite of the apparent plausibility of the conjectures, we will prove that both are false. Consequences with respect to the behavior of standard quasi-Newton methods will be derived. (AU) | |
| Processo FAPESP: | 18/24293-0 - Métodos computacionais de otimização |
| Beneficiário: | Sandra Augusta Santos |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria |
| Beneficiário: | Francisco Louzada Neto |
| Modalidade de apoio: | Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs |