Lectures on Finite Precision Computations

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SIAM, 1996 - Mathematics - 235 pages
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Devoted to the assessment of the quality of numerical results produced by computers, this book addresses the question: How does finite precision affect the convergence of numerical methods on the computer when convergence has been proven in exact arithmetic? Finite precision computations are at the heart of the daily activities of many engineers and researchers in all branches of applied mathematics. Written in an informal style, the book combines techniques from engineering and mathematics to describe the rigorous and novel theory of computability in finite precision. In the challenging cases of nonlinear problems, theoretical analysis is supplemented by software tools to explore the stability on the computer. Roundoff errors are often considered negatively, as a severe limitation on the purity of exact computations. The authors show how the necessarily finite precision of the computer arithmetic can be turned into an asset to describe physical phenomena.

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Measures of Stability for Regular Problems 39
Computation in the Neighbourhood of a Singularity
Experiments with PRECISE 125
Robustness to Nonnormality
Arithmetic Quality of Reliable Algorithms 71
Software Tools for Roundoff Error Analysis in Algorithms 97
More Numerical Illustrations with PRECISE
The Toolbox PRECISE for MATLAB

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About the author (1996)

Francoise Chatelin is Professor of Mathematics at the University of Toulouse and head of the Qualitative Computing Group at CERFACS. Before moving to CERFACS, she was a professor at the universities of Grenoble and Paris IX Dauphine. She also worked for a decade in the industrial research laboratories of IBM France and Thales, where she was in charge of intensive computing activities. Her areas of expertise include spectral theory for linear operators in Banach spaces and finite precision computation of very large eigenproblems. She currently explores the uncharted domain of mathematical computation that lies beyond real or complex analysis.

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