Approximation Theory, Wavelets and Applications

Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex.
Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.

Preface. A Class of Interpolating Positive Linear Operators: Theoretical and Computational Aspects; G. Allasia. Quasi-Interpolation; E.W. Cheney. Approximation and Interpolation on Spheres; E.W. Cheney. Exploring Covariance, Consistency and Convergence in Padé Approximation Theory; A. Cuyt. Dijkstra's Cyclic Projections Algorithm: the Rate of Convergence; F. Deutsch. Interpolation from a Convex Subset of Hilbert Space: a Survey of Some Recent Results; F. Deutsch. The Angle between Subspaces of a Hilbert Space; F. Deutsch. Neville Elimination and Approximation Theory; M. Gasca, J.M. Peña. Approximation with Weights, the Chebyshev Measure and the Equilibrium Measure; M.V. Golitschek. A One-Parameter Class of B-Splines; Z.F. Koçak, G.M. Phillips. Interpolation on the Triangle and Simplex; S.L. Lee, G.M. Phillips. Knot Removal for Scattered Data; A. le Méhauté. Error Estimates for Approximation by Radial Basic Functions; W. Light, H. Wayne. Wavelets on the Interval; E. Quak, N. Weyrich. Best Approximations and Fixed Point Theorems; S.P. Singh, B. Watson. How to Approximate the Inverse Operator; J. Appell. On Some Averages of Trigonometric Interpolating Operators; M. Campiti, G. Metafune, D. Pallara. On the Zeros Locations of K > 2 Consecutive Orthogonal Polynomials and of their Derivatives; F. Costabile, R. Luceri. Can Irregular Subdivisions Preserve Convexity? S. de Marchi, M.M. Cecchi. On Functions Approximation by Shepart-Type Operators -- a Survey; B. della Vecchia, G. Mastroianni. Wavelet Representation of the Potential Integral Equations; M. Dorobantu. Lyapunov Theorem in Approximation Theory; C. Franchetti. On the Order Monotonicity of the Metric Projection Operator; G. Isac. Pointwise Estimates forMultivariate Interpolation Using Conditionally Positive Definite Functions; J. Levesley. Experiments with a Wavelet Based Image Denoising Method; M. Malfait, D. Roose. Proximity Maps: Some Continuity Results; G. Marino, P. Pietramala. Non-Smooth Wavelets: Graphing Functions Unbounded in Every Interval; D.L. Ragozin, A. Bruce, H.-Y. Gao. On the Possible Wavelet Packets Orthonormal Bases; S. Saliani. A Case Study in Multivariate Lagrange Interpolation; T. Sauer, Y. Xu. Trigonometric Wavelets for Time-Frequency-Analysis; K. Selig. Interpolating Subspaces in Rn; B. Shekhtman. Multivariate Periodic Interpolating Wavelets; F. Sprengel. Finite Element Multiwavelets; V. Strela, G. Strang. Polynomial Wavelets on [-1,1]; M. Tasche. On the Solution of Discretely Given Fredholm Integral Equations over Lines; E. Venturino. De-Noising Using Wavelets and Cross Validation; N. Weyrich, G.T. Warhola. On the Construction of Two Dimensional Spatial Varying FIR Filter Banks with Perfect Reconstruction; X. Xia, B.W. Suter. Recursions for Tchebycheff B-Splines and their Jumps; Y. Xu. Quasi-Interpolation on Compact Domains; J. Levesley, M. Roach. Index.