Ball convergence for a ninth order Newton-type method from quadrature and a domain formulae in Banach space (Q2798828)
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: Ball convergence for a ninth order Newton-type method from quadrature and a domain formulae in Banach space |
scientific article; zbMATH DE number 6568238
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ball convergence for a ninth order Newton-type method from quadrature and a domain formulae in Banach space |
scientific article; zbMATH DE number 6568238 |
Statements
13 April 2016
0 references
local convergence
0 references
majorizing sequences
0 references
recurrent relation
0 references
recurrent functions
0 references
radius of convergence
0 references
Fréchet derivative
0 references
quadrature formulae
0 references
Adomian decomposition
0 references
nonlinear operator equation
0 references
iterative method
0 references
Banach space
0 references
multipoint Newton-like method
0 references
error bound
0 references
numerical example
0 references
Ball convergence for a ninth order Newton-type method from quadrature and a domain formulae in Banach space (English)
0 references
The authors study the local convergence of a ninth-order iterative method for approximating a locally unique solution of nonlinear equations defined between two Banach spaces. The aforementioned method is a multipoint Newton-like method, that involves only first derivatives. In addition, the convergence analysis only uses the first Fréchet derivative and not the second one, as it is quite usual in other studies. This work also provides computable convergence balls and error bounds. The paper finishes with some numerical examples to illustrate the theoretical results.
0 references
