Ebook: 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.

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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 Pad? 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.

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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 Pad? 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.

Content:
Front Matter....Pages i-xxiii
A Class of Interpolating Positive Linear Operators: Theoretical and Computational Aspects....Pages 1-36
Quasi-Interpolation....Pages 37-45
Approximation and Interpolation on Spheres....Pages 47-53
Exploring Covariance, Consistency and Convergence in Pade Approximation Theory....Pages 55-86
Dykstra’s Cyclic Projections Algorithm: The Rate of Convergence....Pages 87-94
Interpolation from a Convex Subset of Hilbert Space: A Survey of Some Recent Results....Pages 95-105
The Angle Between Subspaces of a Hilbert Space....Pages 107-130
Neville Elimination and Approximation Theory....Pages 131-151
Approximation with Weights, the Chebyshev Measure and the Equilibrium Measure....Pages 153-167
A One-Parameter Class of B-Splines....Pages 169-176
Interpolation on the Triangle and Simplex....Pages 177-196
Knot Removal for Scattered Data....Pages 197-213
Error Estimates for Approximation by Radial Basis Functions....Pages 215-246
Wavelets on the Interval....Pages 247-283
Best Approximations and Fixed Point Theorems....Pages 285-294
How to Approximate the Inverse Operator....Pages 295-302
On some Averages of Trigonometric Interpolating Operators....Pages 303-313
On the Zeros Localization of K>2 Consecutive Orthogonal Polynomials and of Their Derivatives....Pages 315-324
Can Irregular Subdivisions Preserve Convexity?....Pages 325-334
On Functions Approximation by Shepard-Type Operators — A Survey....Pages 335-346
Wavelet Representation of the Potential Integral Equations....Pages 347-356
Liapunov Theorem in Approximation Theory....Pages 357-364
On the Order Monotonicity of the Metric Projection Operator....Pages 365-379
Pointwise Estimates for Multivariate Interpolation Using Conditionally Positive Definite Functions....Pages 381-401
Experiments with a Wavelet Based Image Denoising Method....Pages 403-414
Proximity Maps: Some Continuity Results....Pages 415-421
Non-smooth Wavelets: Graphing functions unbounded on every interval....Pages 423-432
On the Possible Wavelet Packets Orthonormal Bases....Pages 433-442
A Case Study in Multivariate Lagrange Interpolation....Pages 443-452
Trigonometric Wavelets for Time-Frequency-Analysis....Pages 453-464
Multivariate Periodic Interpolating Wavelets....Pages 465-471
Finite Element Multiwavelets....Pages 473-483
Polynomial Wavelets on [-1, 1]....Pages 485-496
On the Solution of Discretely Given Fredholm Integral Equations Over Lines....Pages 497-512
De-Noising Using Wavelets and Cross Validation....Pages 513-522
On the Construction of two Dimensional Spatial Varying fir Filter Banks with Perfect Reconstruction....Pages 523-532
Recursions for Tchebycheff B-Splines and their Jumps....Pages 533-542
Quasi-Interpolation on Compact Domains....Pages 543-555
Eigenvalues and Nonlinear Volterra Equations....Pages 557-566
Back Matter....Pages 567-570
....Pages 571-572