Ebook: Approximation Theory and Spline Functions

A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22-September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including ~1ultivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invi ted speakers, whose contri­ butions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at MeMorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings.

---

---

Content:
Front Matter....Pages i-ix
Products of Polynomials....Pages 1-22
Exchange Algorithms, Error Estimations and Strong Unicity in Convex Programming and Chebyshev Approximation....Pages 23-63
Four Lectures on Multivariate Approximation....Pages 65-87
The Approximation of Certain Functions by Compound Means....Pages 89-95
A Practical Method for Obtaining a Priori Error Bounds in Pointwise and Mean-Square Approximation Problems....Pages 97-125
Surface Spline Interpolation: Basic Theory and Computational Aspects....Pages 127-142
Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions....Pages 143-145
Semi-Norms in Polynomial Approximation....Pages 147-150
On Spaces of Piecewise Polynomials in Two Variables....Pages 151-197
Birkhoff Interpolation on the Roots of Unity....Pages 199-205
Applications of Transformation Theory: A Legacy from Zolotarev (1847–1878)....Pages 207-245
Explicit Algebraic Nth Order Approximations to PI....Pages 247-256
Solving Integral Equations of Nuclear Scattering by Splines....Pages 257-264
H-Sets for Non-Linear Constrained Approximation....Pages 265-270
Operator Pade Approximants: Some ideas behind the theory and a numerical illustration....Pages 271-288
Harmonic Approximation....Pages 289-292
Best Harmonic L1 Approximation to Subharmonic Functions....Pages 293-295
B-Splines on the Circle and Trigonometric B-Splines....Pages 297-325
On Reducing the Computational Error in the Successive Approximations Method....Pages 327-338
Lebesgue Constants Determined by Extremal Sets....Pages 339-348
Error Bounds for Interpolation by Fourth Order Trigonometric Splines....Pages 349-360
Splines and Collocation for Ordinary Initial Value Problems....Pages 361-378
Using Inclusion Theorems to Establish the Summability of Orthogonal Series....Pages 379-396
On Projections in Approximation Theory....Pages 397-417
A Survey of Exterior Asymptotics for Orthogonal Polynomials Associated with a Finite Interval and a Study of the Case of the General Weight Measures....Pages 419-440
Back Matter....Pages 441-453
....Pages 455-466