Results 261 to 270 of about 16,081 (276)
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Convergence ball of a modified secant method for finding zero of derivatives
Applied Mathematics and Computation, 2006The 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
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Enlarging the convergence ball of the method of parabola for finding zero of derivatives
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ioannis K Argyros, Santhosh George
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Convergence criterion and convergence ball of the Newton-type method in Banach space
Journal of Applied Mathematics and Computing, 2008The 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
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A globally convergent ball Stirling method
Applied Numerical Mathematics, 2004A 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
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A Globally Convergent Ball Newton Method
SIAM Journal on Numerical Analysis, 1981A 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 ...
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On the Convergence of Projections of Uniform Distributions on Balls
Theory of Probability & Its Applications, 1991See the review in Zbl 0717.60037.
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Ball convergence theorems for Halley’s method in Banach space
Journal of Applied Mathematics and Computing, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Argyros, Ioannis K., Ren, Hongmin
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Ball convergence of the Newton–Gauss method in Banach space
SeMA Journal, 2016This paper is about the convergence of a fifth-order Newton method for solving nonlinear equations, based on the conditions on the first dervative. Some examples are given to illustrate the theory.
Argyros, Ioannis K. +2 more
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Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
SeMA Journal, 2015The 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.
Á. Alberto Magreñán +1 more
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2021
Summary: There is a plethora of third and fourth convergence order algorithms for solving Banach space valued equations. These orders are shown under conditions on higher than one derivatives not appearing on these algorithms. Moreover, error estimations on the distances involved or uniqueness of the solution results if given at all are also based on ...
Argyros, Gus +3 more
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Summary: There is a plethora of third and fourth convergence order algorithms for solving Banach space valued equations. These orders are shown under conditions on higher than one derivatives not appearing on these algorithms. Moreover, error estimations on the distances involved or uniqueness of the solution results if given at all are also based on ...
Argyros, Gus +3 more
openaire +2 more sources