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Order stars is a recently developed technique to analyze and
explain the behaviour of numerical methods. The main idea is to
explore different features of numerical algorithms as properties of
analytical functions in various portions of the complex plane.
Thus, for example, the order of some numerical methods for ordinary
differential equations can be translated to the language of
approximation theory - specifically, to the question of how well a
given rational function R approximates the exponential. Likewise,
stability properties of the underlying method can be expressed as
some other features of the function R. In this formulation, order
stars establish the relationship between order and stability,
helping in the search for better and more efficient computational
algorithms.
Michael Powell is one of the world's foremost figures in numerical
analysis. This volume is derived from invited talks given at a
meeting celebrating his 60th birthday and, reflecting Powell's own
achievements, focuses on innovative work in optimization and in
approximation theory. The individual papers have been written by
leading authorities in their subjects and are a mix of expository
articles and surveys on new work. They have all been reviewed and
edited to form a volume that represents the state of the art in an
important discipline within mathematics, with highly relevant
applications throughout science and engineering.
Acta Numerica is a high-impact factor, prestigious annual
publication containing invited surveys by leading researchers in
numerical mathematics and scientific computing. The surveys present
overviews of developments in their area and provide techniques and
analyses. It is essential reading for practitioners and
researchers. It is essential reading for all practitioners and
researchers.
Michael Powell is one of the world's foremost figures in numerical
analysis. This volume, first published in 1997, is derived from
invited talks given at a meeting celebrating his 60th birthday and,
reflecting Powell's own achievements, focuses on innovative work in
optimisation and in approximation theory. The individual papers
have been written by leading authorities in their subjects and are
a mix of expository articles and surveys. They have all been
reviewed and edited to form a coherent volume for this important
discipline within mathematics, with highly relevant applications
throughout science and engineering.
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