About the book

The theory of point estimation, introduced by Smale in 1986, treats convergence conditions and the domain of convergence of iterative methods for solving equations and system of equations. In this book some questions related to the problem of the choice of initial approximations which provide a safe convergence of iterative methods are considered. The main attention is paid to iterative methods for finding polynomial zeros.

The book consists of seven chapters. Some basic concepts and Smale's theory for Newton's method together with its modifications are presented in the first part of the book. The second part contains recent authors' results concerning the construction of initial conditions which guarantee convergence of a wide class of iterative methods for solving algebraic equations. These conditions are computationally verifiable and have a simple form so that they are of practical importance. In particular, initial conditions ensuring convergence of iterative methods for the inclusion of polynomial zeros are established in the last chapter.

Contents

• Iterative methods for solving equations
• Interval methods
• Point estimation theory
• Approximate zeros
• Guaranteed convergence
• Polynomial zeros
• 118 references, Name index and Subject index

The book is both a text and a reference source for mathematicians, engineers, physicists and a computer scientists who are interested in new development and applications, but the material is also accessible to anyone with graduate level mathematical background and some knowledge of basic computational complex analysis.