Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0942.65057
Wang, Xinghua
Convergence of Newton's method and uniqueness of the solution of equations in Banach space. (English)
[J] IMA J. Numer. Anal. 20, No.1, 123-134 (2000). ISSN 0272-4979; ISSN 1464-3642/e

For the well-known Newton-Kantorovich method for solving nonlinear equations in Banach spaces, $f(x)= 0$ in $X$, the author gives exact estimates of convergence and uniqueness balls.\par If $f$ is continuously differentiable in some ball around an exact solution $x^*$ and if $f'(x^*)^{-1}f'$ satisfies a so-called radius Lipschitz condition with the $L$ average, then the method is shown to be convergent for all starting points chosen in this ball. The optimal choice of the radius of this ball is also analyzed.\par Under a so-called centre Lipschitz condition with the $L$ average, the author obtains uniqueness and again demonstrates the optimal choice of the radius.
[E.Emmrich (Berlin)]

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)

Keywords: Newton-Kantorovich method; nonlinear equations; Banach spaces; convergence; Lipschitz condition; uniqueness

Cited in: Zbl pre05853252 Zbl 1176.65061 Zbl 1151.65044 Zbl 1072.65077 Zbl 1027.65078

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]