Surface Fitting and Multiresolution Methods

A. Le Méhauté, C. Rabut, and L. L. Schumaker (eds.)

Vanderbilt University Press, 1997, 353 pp.

ISBN 0-8265-1294-1

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Fast Evaluation of Cardinal Radial Basis Interpolants G. Allasia and P. Giolito . . . . . . . . . . . . . . . . . . . . . 1

Scaled Pivoting and Error Bounds for Totally Positive Linear Systems P. Alonso, M. Gasca and J. M. Peña . . . . . . . . . . . . . . . 9

Reproducing Kernels of Vector-Valued Function Spaces L. Amodei . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Multivariate Mean Value Interpolation A. Augel . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

The Error in Polynomial Tensor-Product, and in Chung-Yao, Interpolation

C. de Boor . . . . . . . . . . . . . . . . . . . . . . . . . 35

A Study of Biorthogonal Sinusoidal Wavelets C. K. Chui and X. Shi . . . . . . . . . . . . . . . . . . . . . 51

Quasi-Interpolant Spline Functions in the Hilbert Space D^{−m}L^{2}(IR) C. Conti . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

An Application of Multiwavelet Analysis to Signal Compression M. Cotronei and L. Puccio . . . . . . . . . . . . . . . . . . . 75

Biorthogonal Box Spline Wavelet Bases S. Dahlke, K. Gröchenig and V. Latour . . . . . . . . . . . . . 83

Wavelets in Numerical Analysis and their Quantitative Properties W. Dahmen, A. Kunoth and K. Urban . . . . . . . . . . . . . 93

Solving Partial Differential Equations by Collocation with Radial Basis Functions

G. E. Fasshauer . . . . . . . . . . . . . . . . . . . . . . . 131

Thinning, Inserting, and Swapping Scattered Data M. S. Floater and A. Iske . . . . . . . . . . . . . . . . . . . 139 Constructing Pairs of Refinable Bivariate Spline Functions

T. N. T. Goodman . . . . . . . . . . . . . . . . . . . . . . 145

Interpolating and Approximating Scattered 3D Data with Hierarchical Tensor Product B-Splines

G. Greiner and K. Hormann . . . . . . . . . . . . . . . . . 163

Wavelet Decomposition for Toeplitz Matrices C. Guerrini and L. B. Montefusco . . . . . . . . . . . . . . . . 173

Interpolation by New Families of B-splines on Uniform Meshes of the Plane

X. Guillet . . . . . . . . . . . . . . . . . . . . . . . . . 183

Topics in Scattered Data Interpolation and Non-Uniform Sampling K. Jetter and J. Stöckler . . . . . . . . . . . . . . . . . . . . 191

Adaptive and Linearly Independent Multilevel B-Splines R. Kraft . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Smooth Interpolation by a Convexity Preserving Nonlinear Subdivision Algorithm

F. Kuijt and R. van Damme . . . . . . . . . . . . . . . . . 219

Open Problems of Approximation G. G. Lorentz . . . . . . . . . . . . . . . . . . . . . . . . 225

Nonexistence of Compactly Supported Box Spline Prewavelets in Sobolev Spaces

R. A. Lorentz and P. Oswald . . . . . . . . . . . . . . . . . 235

Sobolev Norm Convergence of Stationary Subdivision Schemes C. Micchelli and T. Sauer . . . . . . . . . . . . . . . . . . . 245

Discrete Orthogonal Transforms and M-band Wavelets for Image Compression

L. B. Montefusco and D. Lazzaro . . . . . . . . . . . . . . . 261

Optimal Partitions in Bivariate Segment Approximation G. Nürnberger . . . . . . . . . . . . . . . . . . . . . . . . 271

Approximating By Ridge Functions A. Pinkus . . . . . . . . . . . . . . . . . . . . . . . . . . 279

On Stability of Scaling Vectors G. Plonka . . . . . . . . . . . . . . . . . . . . . . . . . . 293

On a Spline Multiresolution Analysis with Homogeneous Boundary Conditions

E. Quak . . . . . . . . . . . . . . . . . . . . . . . . . . 301

On the Efficiency of Interpolation by Radial Basis Functions R. Schaback . . . . . . . . . . . . . . . . . . . . . . . . . 309 Functional Data Fitting and Fairing with Triangular B-Splines

H.-P. Seidel . . . . . . . . . . . . . . . . . . . . . . . . . 319

Nonlinear Approximation with Walsh Atoms L. F. Villemoes . . . . . . . . . . . . . . . . . . . . . . . . 329

Sobolev-type Error Estimates for Interpolation by Radial Basis Functions

H. Wendland . . . . . . . . . . . . . . . . . . . . . . . . 337

Unified IFS-based Model to Generate Smooth or Fractal Forms C. E. Zair and E. Tosan . . . . . . . . . . . . . . . . . . . . 345