Rational Approximation of Real Functions

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Cambridge University Press, Mar 3, 2011 - Mathematics - 384 pages
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Originally published in 1987, this book is devoted to the approximation of real functions by real rational functions. These are, in many ways, a more convenient tool than polynomials, and interest in them was growing, especially since D. Newman's work in the mid-sixties. The authors aim at presenting the basic achievements of the subject and, for completeness, also discuss some topics from complex rational approximation. Certain classical and modern results from linear approximation theory and spline approximation are also included for comparative purposes. This book will be of value to anyone with an interest in approximation theory and numerical analysis.
 

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Contents

Qualitative theory of the best rational approximation
17
Some classical results in the linear theory
40
Approximation of some important functions
73
Converse theorems for rational approximation
161
Spline approximation and Besov spaces
185
Relations between rational and spline approximations
224
Approximation with respect to Hausdorff distance
263
Lower bounds
308
Pade approximations
329
Appendix Some numerical results
348
References
357
Author index
368
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