Complex Interval Arithmetic and Its Applications

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John Wiley & Sons, 1998 - Mathematics - 284 pages
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The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.
 

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Contents

Introduction
9
Interval Arithmetic
15
Circular Complex Inclusion Forms
27
Best Approximations by Disks
52
Inclusion of Polynomial Zeros
90
Simultaneous Inclusion of Complex Zeros
137
Improved Inclusion Methods
180
Parallel Implementation of Inclusion Methods
219
Numerical Stability of Iterative Processes
236
Numerical Computation of Curvilinear Integrals
258
Bibliography
266
Name Index
278
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