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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Contents

Measures of Stability for Regular Problems 39
52
Computation in the Neighbourhood of a Singularity
57
Experiments with PRECISE 125
135
Robustness to Nonnormality
159
Arithmetic Quality of Reliable Algorithms 71
162
Software Tools for Roundoff Error Analysis in Algorithms 97
175
More Numerical Illustrations with PRECISE
199
The Toolbox PRECISE for MATLAB
211
Bibliography
219
Index
233

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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. Her areas of expertise include spectral theory for linear operators in Banach spaces and finite precision computation of very large eigenproblems.

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