Approximation Theory XIV: San Antonio 2013

ISBN-13: 9783319064031 / Angielski / Twarda / 2014 / 395 str.

Gregory E. Fasshauer; Larry L. Schumaker

Opis

These proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included. The book will be of interest to mathematicians, engineers and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.

Spis treści

Isogeometric Method for the Elliptic Monge-Ampère Equation.- Dual Compatible Splines on non Tensor Product Meshes.- Multivariate Anisotropic Interpolation on the Torus.- A Generalized Class of Hard Thresholding Algorithms for Sparse Signal Recovery.- On a New Proximity Condition for Manifold-Valued Subdivision Schemes.- Wachspress and Mean Value Coordinates.- Hermite and Bernstein Style Basis Functions for Cubic Serendipity Spaces on Squares and Cubes.- Suitability of Parametric Shepard Interpolation for Nonrigid Image Registration.- Parabolic Molecules: Curvelets, Shearlets and Beyond.- Microlocal Analysis of Singularities from Directional Multiscale Representations.- Barycentric Interpolation.- Numerical Determination of Extremal Points and Asymptotic Order of Discrete Minimal Riesz Energy for Regular Compact Sets.- Eigenvalue Sequences of Positive Integral Operators and Moduli of Smoothness.- Reconstructing Multivariate Trigonometric Polynomials from Samples Along Rank-1 Lattices.- On Non-degenerate Rational Approximation.- Multivariate C¹-continuous Splines on the Alfeld Split of a Simplex.- On Convergence of Singular Integral Operators with Radial Kernels.- Lower Bound on the Dimension of Trivariate Splines on Cells.- One Characterization of Lagrange Projectors.- Minimal versus Orthogonal Projections onto Hyperplanes in ℓⁿ1 and ℓⁿ_∞.- On Hermite Interpolation by Splines with Continuous Third Derivatives.- Best Polynomial Approximation on the Unit Sphere and the Unit Ball.- Support Vector Machines in Reproducing Kernel Hilbert Spaces versus Banach Spaces.

Blurb

This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.