Results 241 to 250 of about 1,003,682 (268)

Convergence ball of iterations with one parameter

Applied Mathematics, 2005
This article looks at a general family of iterative methods with one parameter to solve the equation \(F(\vec{x})=0\), which includes the super-Halley, the Chebyshev as well as the Halley method. Under a weak Lipschitz condition the author proves a convergence theorem and estimates the convergence radius.
exaly   +3 more sources

Convergence ball of a modified secant method for finding zero of derivatives

Applied Mathematics and Computation, 2006
The authors are concerned with the convergence of a modified secant method which is proposed to find a zero of derivatives of a function \(f\). Under the hypotheses that second order derivatives of \(f\) are Lipschitz continuous, an estimation of the radius of the convergence ball of the modified secant method is presented. More precisely, it is proved
Qingbiao Wu, Hongmin Ren
exaly   +3 more sources

Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations

SeMA Journal, 2015
The local convergence of a method presented by Cordero et al. (see references [10, 12-14] in the paper under review) of convergence order at least five to approximate a locally unique solution of a nonlinear equation is studied. The convergence in this study is shown under hypotheses on the first derivative. The applicability of the method is expanded.
Angel Alberto Magreñán, Ioannis K Argyros   +1 more
exaly   +3 more sources

Enlarging the convergence ball of the method of parabola for finding zero of derivatives

Applied Mathematics and Computation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Santhosh George, Ioannis K Argyros
exaly   +4 more sources

The convergence ball and error analysis of the two-step Secant method

Applied Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yasir Khan, Qingbiao Wu, Minhong Chen
exaly   +2 more sources

Convergence criterion and convergence ball of the Newton-type method in Banach space

Journal of Applied Mathematics and Computing, 2008
The article deals with the following Newton-like iteration \[ x_{n+1} = y_n - f'(x_n)^{-1}f(y_n), \;\;y_n = x_n - f'(x_n)^{-1}f(x_n), \quad n = 0,1,\dots \] for approximate solving the nonlinear operator equation \(f(x) = 0\), where \(f\) is a nonlinear operator between Banach spaces \(E\) and \(F\).
Zhang, Huaren, Li, Weiguo
openaire   +2 more sources

Ball Convergence for eighth order method

2017
Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a Banach space Y. The equation (21.1) covers wide range of problems in classical analysis and applications [1-30]. Closed form solutions
Argyros, Ioannis K, Magreñán, Á. Alberto   +1 more
openaire   +2 more sources

A Globally Convergent Ball Newton Method

SIAM Journal on Numerical Analysis, 1981
A new n-dimensional Newton method is presented. In each step a whole n-dimensional ball is determined rather than a single new approximation point. This ball contains the desired zero of the given function. The method is globally convergent. If the given initial ball does not contain any zero, then the method stops after a finite number of steps ...
openaire   +1 more source

A globally convergent ball Stirling method

Applied Numerical Mathematics, 2004
A Stirling iterative method for solving an operator equation \(P(x)=0\), or equivalently, a fixed point equation \(F(x)=x\) can be viewed as a combination of fixed point iteration and Newton iteration. The iterative scheme \(x_{n+1}=x_n-[I-F'(y_n)]^{-1}[x_n-F(x_n)]\) gives a general class of schemes. For \(y_n=x_n\), one has the standard Newton method,
Sen, Rabindra Nath, Guhathakurta, Pulak
openaire   +1 more source

On the Convergence of Projections of Uniform Distributions on Balls

Theory of Probability & Its Applications, 1991
See the review in Zbl 0717.60037.
openaire   +1 more source