Convergence theorems for Newton-like methods using data from a set or a single point and outer inverses (Q2782154)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Convergence theorems for Newton-like methods using data from a set or a single point and outer inverses |
scientific article; zbMATH DE number 1727699
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence theorems for Newton-like methods using data from a set or a single point and outer inverses |
scientific article; zbMATH DE number 1727699 |
Statements
25 April 2002
0 references
nonlinear operator equations
0 references
Newton-like methods
0 references
outer inverse
0 references
convergence
0 references
Fréchet-derivative
0 references
Convergence theorems for Newton-like methods using data from a set or a single point and outer inverses (English)
0 references
Two theorems are demonstrated concerning the semilocal convergence of Newton-like methods \(x_{n+1}=x_n-A(x_n)^\#F(x_n)\), where \(A\) is an approximation of the Fréchet-derivative \(F'\) and \(A^\#\) is an outer inverse of \(A\), i.e. \(A^\#AA^\#=A^\#\). For the semilocal convergence it is used the information from a set or a single point and outer inverse.
0 references
