Curve and Surface Fitting, St. Malo 1999

Albert Cohen, Christophe Rabut, and Larry L. Schumaker

Vanderbilt University Press, Nashville, 2000

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Extending Lawson’s Algorithm to Include the Huber M-Estimator Iain J. Anderson, John C. Mason, and Colin Ross . . . . . . . . . . 1

A Segmentation Method under Geometric Constraints after Pre-processing

D. Apprato, J. B. Betbeder, C. Gout, and S. Vieira-Teste . . . . . . 9

Building Adaptive Multiresolution Schemes within Harten’s Framework Francesc Aràndiga and Rosa Donat . . . . . . . . . . . . . . . 19

A Recursive Approach to the Construction of k-Balanced Biorthogonal Multifilters

Silvia Bacchelli, Mariantonia Cotronei, and Damiana Lazzaro … 27

Fast Evaluation of Radial Basis Functions: A Multivariate Momentary Evaluation Scheme

R. K. Beatson and E. Chacko . . . . . . . . . . . . . . . . . 37

Polyharmonic Splines in IR^{d}: Tools for Fast Evaluation R. K. Beatson, J. B. Cherrie, and David L. Ragozin . . . . . . . . 47

Constructive Approximation by (V, f)-Reproducing Kernels Mohammed-Najib Benbourhim . . . . . . . . . . . . . . . . . 57

Adaptive Wavelet Galerkin Methods on Distorted Domains: Setup of the Algebraic System

Stefano Berrone and Karsten Urban . . . . . . . . . . . . . . 65

Scattered Data Near-Interpolation with Application to Discontinuous Surfaces

Renata Besenghi and Giampietro Allasia . . . . . . . . . . . . 75

On a Method of Numerical Differentiation Mira Bozzini and Milvia Rossini . . . . . . . . . . . . . . . . 85

Ridgelets and their Derivatives: Representation of Images with Edges Emmanuel J. Candès . . . . . . . . . . . . . . . . . . . . . 95

Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges

Emmanuel J. Candès and David L. Donoho . . . . . . . . . . . 105 Bases in Function Spaces on Compact Sets

Zbigniew Ciesielski . . . . . . . . . . . . . . . . . . . . . . 121

A Note on Convolving Refinable Function Vectors C. Conti and K. Jetter . . . . . . . . . . . . . . . . . . . . . 135

Interpolating Polynomial Macro-Elements with Tension Properties Paolo Costantini and Carla Manni . . . . . . . . . . . . . . . 143

Quantized Frame Decompositions M. Craizer, D. A. Fonini, Jr., and E. A. B. da Silva . . . . . . . . 153

Cubic Spline Interpolation on Nested Polygon Triangulations Oleg Davydov, Günther Nürnberger, and Frank Zeilfelder . . . . . 161

Stable Local Nodal Bases for C^{1} Bivariate Polynomial Splines Oleg Davydov and Larry L. Schumaker . . . . . . . . . . . . . 171

On Lacunary Multiresolution Methods of Approximation in Hilbert Spaces

Lubomir T. Dechevski and Wolfgang L. Wendland . . . . . . . . 181

Interpolation with Curvature Constraints Hafsa Deddi, Hazel Everett, and Sylvain Lazard . . . . . . . . . 191

A B-spline Tensor for Vectorial Quasi-Interpolant Fabrice Dodu . . . . . . . . . . . . . . . . . . . . . . . . . 201

Analysis of Scalar Datasets on Multi-Resolution Geometric Models Alexandre Gerussi and Georges–Pierre Bonneau . . . . . . . . . 209

Biorthogonal Refinable Spline Functions Tim N. T. Goodman . . . . . . . . . . . . . . . . . . . . . 219

Fitting Parametric Curves to Dense and Noisy Points A. Ardeshir Goshtasby . . . . . . . . . . . . . . . . . . . . 227

Smooth Irregular Mesh Interpolation Stefanie Hahmann, Georges-Pierre Bonneau, and Riadh Taleb … 237

Multi–Level Approximation to Scattered Data using Inverse Multiquadrics

S. J. Hales and J. Levesley . . . . . . . . . . . . . . . . . . . 247

Best Approximation Algorithms: A Unified Approach V. V. Kovtunets . . . . . . . . . . . . . . . . . . . . . . . 255

On Curve Interpolation in IR^{d} Jernej Kozak and Emil Žagar . . . . . . . . . . . . . . . . . . 263

Interpolating Involute Curves Mitsuru Kuroda and Shinji Mukai . . . . . . . . . . . . . . . . 273

Interpolation from Lagrange to Holberg Michel Léger . . . . . . . . . . . . . . . . . . . . . . . . . 281 Local Approximation on Manifolds Using Radial Functions and Polynomials

Jeremy Levesley and David L. Ragozin . . . . . . . . . . . . . 291

Characterizations of Native Spaces Lin-Tian Luh . . . . . . . . . . . . . . . . . . . . . . . . . 301

Review of Some Approximation Operators for the Numerical Analysis of Spectral Methods

Yvon Maday . . . . . . . . . . . . . . . . . . . . . . . . 309

H–Bases I: The foundation H. Michael Möller and Thomas Sauer . . . . . . . . . . . . . . 325

H–Bases II: Applications to Numerical Problems H. Michael Möller and Thomas Sauer . . . . . . . . . . . . . . 333

Dependence Structure of Random Wavelet Coefficients in Terms of Cumulants

Philippe Naveau, Peter Brockwell, and Doug Nychka . . . . . . . 343

Interpolating Functions on Lines in 3-Space Martin Peternell and Helmut Pottmann . . . . . . . . . . . . . 351

Numerical Techniques Based on Radial Basis Functions Robert Schaback and Holger Wendland . . . . . . . . . . . . . 359

Parametric Polynomial Curves of Local Approximation Order 8 K. Scherer . . . . . . . . . . . . . . . . . . . . . . . . . . 375

A B–Spline Approach to Hermite Subdivision U. Schwanecke and B. Jüttler . . . . . . . . . . . . . . . . . . 385

An Interpolation Method with Weights and Relaxation Parameters Chiew-Lan Tai, Brian A. Barsky, and Kia-Fock Loe . . . . . . . . 393

On Properties of Contours of Trilinear Scalar Fields Holger Theisel . . . . . . . . . . . . . . . . . . . . . . . . 403

Non-Stationary Subdivision for Inhomogeneous Order Differential Equations

Joe Warren and Henrik Weimer . . . . . . . . . . . . . . . . 411