Ebook: New Developments in Approximation Theory: 2nd International Dortmund Meeting (IDoMAT) ’98, Germany, February 23–27, 1998

This book contains refereed papers which were presented at the Second International Dortmund Meeting on Approximation Theory (IDoMAT ‘98) at Haus Bommerholz, the conference center of Dortmund University, during the week of February 23–27, 1998. At this conference 50 researchers and specialists from Bulgaria, China, France, Great Britain, Hungary, Israel, Italy, Romania, South Africa and Germany participated and described new developments in the fields of univariate and multivariate approximation theory. The papers cover topics such as radial basis functions, bivariate spline interpolation, subdivision algorithms, multilevel interpolation, multivariate triangular Bernstein bases, Padé approximation, comonotone polynomial approximation, weighted and unweighted polynomial approximation, adaptive approximation, approximation operators of binomial type, quasi-interpolants, generalized convexity and Peano kernel techniques.

This research has applications in areas such as computer-aided geometric design, as applied in engineering and medical technology (e.g. computerized tomography).

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Content:
Front Matter....Pages i-8
Feller Semigroups, Bernstein type Operators and Generalized Convexity Associated with Positive Projections....Pages 9-32
Gregory’s Rational Cubic Splines in Interpolation Subject to Derivative Obstacles....Pages 33-47
Interpolation by Splines on Triangulations....Pages 49-70
On the Use of Quasi-Newton Methods in DAE-Codes....Pages 71-77
On the Regularity of Some Differential Operators....Pages 79-86
Some Inequalities for Trigonometric Polynomials and their Derivatives....Pages 87-94
Inf-Convolution and Radial Basis Functions....Pages 95-108
On a Special Property of the Averaged Modulus for Functions of Bounded Variation....Pages 109-116
A Simple Approach to the Variational Theory for Interpolation on Spheres....Pages 117-143
Constants in Comonotone Polynomial Approximation — A Survey....Pages 145-158
Will Ramanujan kill Baker-Gammel-Wills? (A Selective Survey of Pad? Approximation)....Pages 159-174
Approximation Operators of Binomial Type....Pages 175-198
Certain Results Involving Gammaoperators....Pages 199-214
Recent research at Cambridge on radial basis functions....Pages 215-232
Representation of quasi-interpolants as differential operators and applications....Pages 233-253
Native Hilbert Spaces for Radial Basis Functions I....Pages 255-282
Adaptive Approximation with Walsh-similar Functions....Pages 283-302
Dual Recurrence and Christoffel-Darboux-Type Formulas for Orthogonal Polynomials....Pages 303-313
On Some Problems of Weighted Polynomial Approximation and Interpolation....Pages 315-328
Asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights. Some new theorems and applications....Pages 329-339
Back Matter....Pages 341-344

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Content:
Front Matter....Pages i-8
Feller Semigroups, Bernstein type Operators and Generalized Convexity Associated with Positive Projections....Pages 9-32
Gregory’s Rational Cubic Splines in Interpolation Subject to Derivative Obstacles....Pages 33-47
Interpolation by Splines on Triangulations....Pages 49-70
On the Use of Quasi-Newton Methods in DAE-Codes....Pages 71-77
On the Regularity of Some Differential Operators....Pages 79-86
Some Inequalities for Trigonometric Polynomials and their Derivatives....Pages 87-94
Inf-Convolution and Radial Basis Functions....Pages 95-108
On a Special Property of the Averaged Modulus for Functions of Bounded Variation....Pages 109-116
A Simple Approach to the Variational Theory for Interpolation on Spheres....Pages 117-143
Constants in Comonotone Polynomial Approximation — A Survey....Pages 145-158
Will Ramanujan kill Baker-Gammel-Wills? (A Selective Survey of Pad? Approximation)....Pages 159-174
Approximation Operators of Binomial Type....Pages 175-198
Certain Results Involving Gammaoperators....Pages 199-214
Recent research at Cambridge on radial basis functions....Pages 215-232
Representation of quasi-interpolants as differential operators and applications....Pages 233-253
Native Hilbert Spaces for Radial Basis Functions I....Pages 255-282
Adaptive Approximation with Walsh-similar Functions....Pages 283-302
Dual Recurrence and Christoffel-Darboux-Type Formulas for Orthogonal Polynomials....Pages 303-313
On Some Problems of Weighted Polynomial Approximation and Interpolation....Pages 315-328
Asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights. Some new theorems and applications....Pages 329-339
Back Matter....Pages 341-344
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