Journal ArticleDOI
Über mehrstufige Iterationsverfahren und die Lösung der Hammersteinschen Gleichung
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The numerical solution of integral equations of Hammerstein type results in solving systems of equationsx+Kf(x)=0 with constant matrixK and diagonal mappingf. as mentioned in this paper showed that two-step iterative methods are asymptotically optimal if K is positive semi-definite and f is isotone and continuously differentiable.Abstract:
The numerical solution of integral equations of Hammerstein type results in solving systems of equationsx+Kf(x)=0 with constant matrixK and diagonal mappingf. It is shown that two-step iterative methods are asymptotically optimal ifK is positive semi-definite andf is isotone and continuously differentiable.read more
Citations
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Journal ArticleDOI
Stationary and almost stationary iterative (k, l)-step methods for linear and nonlinear systems of equations
TL;DR: In this paper, it was shown that the residual polynomials of a stationary semi-iterative (k, l)-step method are generalized Faber polynomial with respect to a particular weight function.
Journal ArticleDOI
K-step iterative methods for solving nonlinear systems of equations
TL;DR: In this article, it was shown that k-step stationary iterative methods may converge locally even in cases where the usual iteration of the iterative process diverges, and the results were extended to nonstationary methods of type (2) and cyclic mappings.
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Iterative k-step methods for computing possibly repulsive fixed points in banach spaces
Martin H. Gutknecht,André Kaiser +1 more
TL;DR: In this article, an iterative method for computing a fixed point x ∗ of a Frechet-differentiable self-mapping of a sub-set in a Banach space is discussed.
References
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Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Journal ArticleDOI
Some methods of speeding up the convergence of iteration methods
TL;DR: In this article, the authors consider the problem of minimizing the differentiable functional (x) in Hilbert space, so long as this problem reduces to the solution of the equation grad(x) = 0.