Ebook: Approximation Theory, Spline Functions and Applications

These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and up-to-date developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni­ variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor­ tant subject. The work involves key techniques in approximation theory­ cardinal splines, B-splines, Euler-Frobenius polynomials, spline spaces with non-uniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im­ age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang­ Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit­ tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas­ cale, R. Charron, and B.

---

---

Content:
Front Matter....Pages i-xvi
Approximation By Functions of Nonclassical Form....Pages 1-18
Wavelets — With Emphasis on Spline-Wavelets and Applications to Signal Analysis....Pages 19-39
Pade Approximation in One and More Variables....Pages 41-68
Rational Hermite Interpolation in One and More Variables....Pages 69-103
The Method of Alternating Orthogonal Projections....Pages 105-121
Selections For Metric Projections....Pages 123-137
Weighted Polynomials....Pages 139-161
Some Aspects of Radial Basis Function Approximation....Pages 163-190
A Tutorial on Multivariate Wavelet Decomposition....Pages 191-212
Using The Refinement Equation For The Construction of Pre-Wavelets VI: Shift Invariant Subspaces....Pages 213-222
Error Estimates For Near-Minimax Approximations....Pages 223-241
Different Metrics and Location Problems....Pages 243-253
On The Effectiveness of Some Inversion Methods For Noisy Fourier Series....Pages 255-267
A Generalization of N-Widths....Pages 269-278
Korovkin Theorems For Vector-Valued Continuous Functions....Pages 279-292
On Modified Bojanic-Shisha Operators....Pages 293-302
A Property of Zeros and Cotes Numbers of Hermite and Laguerre Orthogonal Polynomials....Pages 303-310
Hermite-Fej?a and Hermite Interpolation....Pages 311-316
New Results on Lagrange Interpolation....Pages 317-331
Ambiguous Loci in Best Approximation Theory....Pages 333-340
A Theorem on Best Approximations in Topological Vector Spaces....Pages 341-349
On the Characterization of Totally Positive Matrices....Pages 351-355
Iterative Methods For the General Order Complementarity Problem....Pages 357-364
Wavelets, Splines and Divergence-Free Vector Functions....Pages 365-380
An Approach to Meromorphic Approximation in a Stein Manifold....Pages 381-390
Approximating Fixed Points For Nonexpansive Maps in Hubert Spaces....Pages 391-403
On Approximation and Interpolation of Convex Functions....Pages 405-409
Convergence of Approximating Fixed Point Sets For Multivalued Nonexpansive Mappings....Pages 411-418
A Subdivision Algorithm For Non—Uniform B—Splines....Pages 419-422
Approximation Theorem For Fixed Points of Multi-Valued Contractions....Pages 423-436
Geometrical Differentiation and High—Accuracy Curve Interpolation....Pages 437-444
On Best Simultaneous Approximation in Normed Linear Spaces....Pages 445-462
Some Examples Concerning Projection Constants....Pages 463-470
Back Matter....Pages 471-476
....Pages 477-479