Trends and Applications in Constructive Approximation

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Springer Science & Business Media, May 19, 2005 - Mathematics - 281 pages
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During the last years, constructive approximation has reached out to enc- pass the computational and approximation-theoretical aspects of di?erent ?elds in applied mathematics, including multivariate approximation methods, qua- interpolation, and multivariate approximation by (orthogonal) polynomials, as well as modern mathematical developments in neuro fuzzy approximation, R- networks, industrial and engineering applications. Following the tradition of our internationalBommerholz conferencesin 1995, 1998, and 2001 we regard this 4th IBoMAT meeting as an important possibility for specialists in the ?eld of applied mathematics to communicateabout new ideas with colleaguesfrom 15 di?erent countries all over Europe and as far awayas New Zealand and the U.S.A. The conference in Witten Bommerholz was, as always, held in a very friendly and congenial atmosphere. The IBoMAT-series editor Detlef H. Mache (Bochum) would like to congr- ulate Marcel de Bruin (Delft) and Joz sef Szabados (Budapest) for an excellent editing job of this 4th volume about Trends and Applications in constructive - proximation. After the previous three published books in Akademie Verlag (1995) and Birkh] auser Verlag (1999 and 2003) we were pleased with the high quality of the contributions which could be solicited for the book. They are refereed and we should mention our gratitude to the referees and their reports."
 

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Contents

Best Poisson Approximation of Poisson Mixtures A Linear Operator Approach
1
On Some Classes of Diffusion Equations and Related Approximation Problems
13
Recent Developments in Barycentric Rational Interpolation
27
Approximation on Simplices and Orthogonal Polynomials
53
A General Method for Regularity
61
Sufficient Convergence Conditions for Certain Accelerated Successive Approximations
71
The Combined ShepardLidstone Bivariate Operator
77
Local RBF Approximation for Scattered Data Fitting with Bivariate Splines
91
A MarkovBernstein Inequality for Gaussian Networks
165
TS Control The Link between Fuzzy Control and Classical Control Theory
181
Polynomial Bases for Continuous Function Spaces
195
Novel Simulation Approaches for Cyclic Steadystate Fixedbed Processes Exhibiting Sharp Fronts and Shocks
207
Semigroups Associated to Mache Operators II
225
Recent Progress on Univariate and Multivariate Polynomial and Spline Quasiinterpolants
229
A Strong Converse Result for Approximation by Weighted Bernstein Polynomials on the Real Line
247
Rprop Using the Natural Gradient
259

The Use of Strategy Adaptation
103
Finding Relevant Input Arguments with Radial Basis Function Networks
125
Subdivision Schemes and Non Nested Grids
135
Some Properties of Quasiorthogonal and Paraorthogonal Polynomials A Survey
273
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Page 11 - U., On the uniform modulus of continuity of certain discrete approximation operators, J. Approx. Theory 54 (1988), 326-337 [4] PYCH-TABERSKA P., Properties of some discrete approximation operators in weighted function spaces, Commentationes Math.