Point Estimation of Root Finding Methods

1. Front Matter

   Pages i-xii

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2. Basic Concepts

   Pages 1-34

3. Iterative Processes and Point Estimation Theory

   Pages 35-66

4. Point Estimation of Simultaneous Methods

   Pages 67-127

5. Families of Simultaneous Methods of Higher Order: Part I

   Pages 129-160

6. Families of Simultaneous Methods of Higher Order: Part II

   Pages 161-195

7. Back Matter

   Pages 197-210

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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.

• Newton's method
• guaranteed convergence
• iterative root finders
• point estimation
• polynomial zeros
• solving nonlinear equations

• Department of Mathematics Faculty of Electronic Engineering, University of Niš, Niš, Serbia

  Miodrag Petković

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