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WILEY-VCH, Mathematical Research, Vol. 105, 1998


Miodrag S. Petković, University of Niš, Serbia
Ljiljana D. Petković, University of Niš, Serbia

ISBN: 3-527-40134-2

284 pages

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