Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations (Q1683028)
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: Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations |
scientific article; zbMATH DE number 6816133
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations |
scientific article; zbMATH DE number 6816133 |
Statements
Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations (English)
0 references
6 December 2017
0 references
Necessary and sufficient conditions for two-and three-point iterative methods to have the convergence order \(p\) \((2 \leq p \leq 8)\) are received. Simple sets of parameters of the iterative procedures are proposed that make it possible to increase the order of convergence. Results of many numerical experiments are obtained.
0 references
nonlinear equations
0 references
Newton-type iterations
0 references
order of convergence
0 references
optimal order
0 references
numerical experiment
0 references
0 references
0 references
0.8995201
0 references
0.8990792
0 references
0.8942599
0 references
0.89026785
0 references
0.89009434
0 references
0.8896451
0 references
0.88781655
0 references
0.8872369
0 references
