EAN: 9783540778509

POINT ESTIMATION OF ROOT FINDING METHODS - MIOD...

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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