Results 161 to 170 of about 4,814 (186)

Secant-type methods and nondiscrete induction

Numerical Algorithms, 2012
For solving the equation \(f(x)= 0\), where \(f\) is a Fréchet-differentiable operator defined on a subset \(D\) of a Banach space \(X\) with values in a Banach space \(Y\), the authors consider secant-type methods based on the concept of nondiscrete mathematical induction.
Ioannis K. Argyros, Saïd Hilout
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A note on the secant method

BIT, 1975
It is conjectured that the secant method converges linearly to a root of multiplicitym. In support of this, it is proved that the linearized secant method produces a bounded sequence of approximations except for a restricted set of values of the two initial approximations.
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Extending the applicability of Secant methods and nondiscrete induction

Applied Mathematics and Computation, 2011
Nondiscrete mathematical induction is used to extend the applicability of secant methods for solving nonlinear operator equations in a Banach space setting. This approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more ...
Ioannis K. Argyros, Saïd Hilout
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The Secant Method and the Golden Mean

The American Mathematical Monthly, 1993
The rate at which the sequence {Xk} converges to a root a depends on the multiplicity of a. Recall that a is a root of multiplicity m of the function f if f(x) can be written as f(x) (x a) m(x), where 4 is bounded at a and ( a) = 0. (2) It is well known (see [2]) that if a is simple root, that is, if m = 1, then there will be a nonzero asymptotic error
Melvin J. Maron, Robert J. Lopez
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An interval version of the secant method

BIT, 1984
The paper is mainly concerned with a modification of the secant method which is based on interval arithmetic ideas. Interval arithmetic is used to force global convergence of any local zero finder without sacrifying convergence speed. Unfortunately no numerical examples are given.
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Modified Secant-type methods for unconstrained optimization

Applied Mathematics and Computation, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convergence theory for the structured BFGS secant method with an application to nonlinear least squares

Journal of Optimization Theory and Applications, 1989
J E Dennis, Hector J Martinez, R A Tapia
exaly  

Improving the applicability of the secant method to solve nonlinear systems of equations

Applied Mathematics and Computation, 2014
Sérgio Amat, M A Hernández-Verón, M J Rubio   +2 more
exaly  

A new family of Secant-like method with super-linear convergence

Applied Mathematics and Computation, 2005
V Kanwar, Janak Raj Sharma
exaly  

Secant modification of Newton's method

Communications of the ACM, 1958
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