Newton's method and high-order algorithms for the \(n\)th root computation (Q2519695)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Newton's method and high-order algorithms for the \(n\)th root computation |
scientific article |
Statements
Newton's method and high-order algorithms for the \(n\)th root computation (English)
0 references
27 January 2009
0 references
The author constructs affine combinations of \(p\)-th order convergent modifications of Newton's method for the computation of the \(n\)-th root of a positive scalar number. It is shown that an appropriate choice of the parameters of the affine combination gives rise to iterative schemes that are convergent of order up to \(p+3\).
0 references
\(n\)-th root
0 references
Newton's method
0 references
high-order methods
0 references
convergence
0 references
