Approximation Theory X: Wavelets, Splines, and Applications

Charles K. Chui, Larry L. Schumaker, and Joachim Stöckler (eds.)

Vanderbilt University Press, Nashville, 2002

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

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

C^{1} Quintic Spline Interpolation over Tetrahedral Partitions Gerard Awanou and Ming-Jun Lai . . . . . . . . . . . . . . 1

Good Point/Bad Point Iterations for Solving the Thin–Plate Spline Interpolation Equations

R. K. Beatson and J. Levesley . . . . . . . . . . . . . . . . 17

On Semi-Cardinal Interpolation for Biharmonic Splines Aurelian Bejancu . . . . . . . . . . . . . . . . . . . . . . 27

Gabor Frames with Arbitrary Windows Kai Bittner and Charles K. Chui . . . . . . . . . . . . . . . 41

Nonseparable Wavelet Packets Lasse Borup and Morten Nielsen . . . . . . . . . . . . . . . 51

The Wavelet Dimension Function for Real Dilations and Dilations Admitting Non-MSF Wavelets

Marcin Bownik and Darrin Speegle . . . . . . . . . . . . . 63

New Ties between Computational Harmonic Analysis and Approximation Theory

Emmanuel J. Candès . . . . . . . . . . . . . . . . . . . . 87

Approximation of the Eigenvalues of Regular Fourth Order Sturm–Liouville Problems Using Interpolation Theory

B. Chanane . . . . . . . . . . . . . . . . . . . . . . . 155

Introduction to Synthetic Aperture Radar (SAR) and SAR Interferometry

Margaret Cheney . . . . . . . . . . . . . . . . . . . . 167

Supports of Multivariate Refinable Functions Hoi Ling Cheung and Canqin Tang . . . . . . . . . . . . . 179

Tight Frames with Maximum Vanishing Moments and Minimum Support

Charles K. Chui, Wenjie He, and Joachim Stöckler . . . . . . 187 Nonstationary Wavelets and Refinement Sequences of Nonuniform B-splines

Charles K. Chui and Jian-ao Lian . . . . . . . . . . . . . 207

Locally Stable Spline Bases on Nested Triangulations Oleg Davydov . . . . . . . . . . . . . . . . . . . . . . 231

Numerical Optimization of Financial Portfolios Uwe Depczynski . . . . . . . . . . . . . . . . . . . . . 241

Quadratic Convergence of Newton’s Method for Constrained Interpolation

Asen L. Dontchev, Houduo Qi, and Liqun Qi . . . . . . . . 261

Matrix-free Multilevel Moving Least-Squares Methods Gregory E. Fasshauer . . . . . . . . . . . . . . . . . . . 271

Shape–preserving, Multiscale Fitting of Bivariate Data by Cubic L_{1} Smoothing Splines

David E. Gilsinn and John E. Lavery . . . . . . . . . . . 283

Orthogonal Spline Projections for Linear Boundary Value Problems

Manfred v. Golitschek . . . . . . . . . . . . . . . . . . 295

Stable Refinable Generators of Shift Invariant Spaces with Certain Regularities and Vanishing Moments

Tian-Xiao He . . . . . . . . . . . . . . . . . . . . . . 305

A Short-support Dual Mask to the Piecewise Linears on a Uniform Triangulation

Bruce Kessler . . . . . . . . . . . . . . . . . . . . . . 323

Wavelet Analysis of Cardinal L–Splines and Construction of Multivariate Prewavelets

Ognyan Kounchev and Hermann Render . . . . . . . . . . 333

Discrete GB-Splines and Their Properties Boris I. Kvasov . . . . . . . . . . . . . . . . . . . . . . 355

Parameterizations of Univariate Orthogonal Wavelets with Short Support

Ming-Jun Lai and David W. Roach . . . . . . . . . . . . 369

Bivariate C^{1} Cubic Splines for Exterior Biharmonic Equations

Ming-Jun Lai, Paul Wenston and Lung-an Ying . . . . . . . 385

Lagrange Interpolation by C^{1} Cubic Splines on Triangulations of Separable Quadrangulations

Günther Nürnberger, Larry L. Schumaker, and Frank Zeilfelder 405 Framelets with Many Vanishing Moments

Alexander Petukhov . . . . . . . . . . . . . . . . . . . . 425

Stability of Radial Basis Function Interpolants Robert Schaback . . . . . . . . . . . . . . . . . . . . . 433

Extremal Properties of Conditionally Positive Definite Functions

Hans Strauss . . . . . . . . . . . . . . . . . . . . . . 441

On Linear Independence of Generators of FSI Distribution Spaces on IR

Jianzhong Wang . . . . . . . . . . . . . . . . . . . . . 453

Fast Evaluation of Radial Basis Functions: Methods Based on Partition of Unity

Holger Wendland . . . . . . . . . . . . . . . . . . . . 473