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Books > Science & Mathematics > Mathematics > Algebra
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Iterative Methods for Simultaneous Inclusion of Polynomial Zeros (Paperback, 1989 ed.)
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Iterative Methods for Simultaneous Inclusion of Polynomial Zeros (Paperback, 1989 ed.)
Series: Lecture Notes in Mathematics, 1387
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The simultaneous inclusion of polynomial complex zeros is a crucial
problem in numerical analysis. Rapidly converging algorithms are
presented in these notes, including convergence analysis in terms
of circular regions, and in complex arithmetic. Parallel circular
iterations, where the approximations to the zeros have the form of
circular regions containing these zeros, are efficient because they
also provide error estimates. There are at present no book
publications on this topic and one of the aims of this book is to
collect most of the algorithms produced in the last 15 years. To
decrease the high computational cost of interval methods, several
effective iterative processes for the simultaneous inclusion of
polynomial zeros which combine the efficiency of ordinary
floating-point arithmetic with the accuracy control that may be
obtained by the interval methods, are set down, and their
computational efficiency is described. The rate of these methods is
of interest in designing a package for the simultaneous
approximation of polynomial zeros, where automatic procedure
selection is desired. The book is both a text and a reference
source for mathematicans, engineers, physicists and computer
scientists who are interested in new developments and applications,
but the material is also accessible to anyone with graduate level
mathematical background and some knowledge of basic computational
complex analysis and programming.
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