EAN: 9783540778509

Bilder-Quelle: discount24.de - Sport-Freizeit

The problem of solving nonlinear equations and systems of equations ranks among the most signi?cant in the theory and practice not only of applied mathematicsbutalsoofmanybranchesofengineeringsciences physics c- puter science astronomy ?nance and so on. A glance at the bibliography and the list of great mathematicians who have worked on this topic points to a high level of contemporary interest. Although the rapid development of digital computers led to the e?ective implementation of many numerical methods in practical realization it is necessary to solve various problems such as computational e?ciency based on the total central processor unit time the construction of iterative methods which possess a fast convergence in the presence of multiplicity (or clusters) of a desired solution the control of rounding errors information about error bounds of obtained approximate solution stating computationally veri?able initial conditions that ensure a safe convergence etc. It is the solution of these challenging problems that was the principal motivation for the present study. In this book we are mainly concerned with the statement and study of initial conditions that provide the guaranteed convergence of an iterative method for solving equations of the form f(z) = 0. The traditional approach to this problem is mainly based on asymptotic convergence analysis using some strong hypotheses on di?erentiability and derivative bounds in a rather wide domain.

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19.03.2025 um 15:01 Uhr

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