Approximation Theory and Spline Functions

1. Front Matter

   Pages i-ix

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2. Products of Polynomials

   • Bernard Beauzamy

   Pages 1-22

3. Exchange Algorithms, Error Estimations and Strong Unicity in Convex Programming and Chebyshev Approximation

   • Hans-Peter Blatt

   Pages 23-63

4. Four Lectures on Multivariate Approximation

   • E. W. Cheney

   Pages 65-87

5. The Approximation of Certain Functions by Compound Means

   • D. M. E. Foster, G. M. Phillips

   Pages 89-95

6. A Practical Method for Obtaining a Priori Error Bounds in Pointwise and Mean-Square Approximation Problems

   • Jean Meinguet

   Pages 97-125

7. Surface Spline Interpolation: Basic Theory and Computational Aspects

   • Jean Meinguet

   Pages 127-142

8. Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions

   • Charles A. Micchelli

   Pages 143-145

9. Semi-Norms in Polynomial Approximation

   • G. M. Phillips, P. J. Taylor

   Pages 147-150

10. On Spaces of Piecewise Polynomials in Two Variables

    • Larry L. Schumaker

    Pages 151-197

11. Birkhoff Interpolation on the Roots of Unity

    • A. Sharma

    Pages 199-205

12. Applications of Transformation Theory: A Legacy from Zolotarev (1847–1878)

    • John Todd

    Pages 207-245

13. Explicit Algebraic Nth Order Approximations to PI

    • J. M. Borwein, P. B. Borwein

    Pages 247-256

14. Solving Integral Equations of Nuclear Scattering by Splines

    • M. Brannigan

    Pages 257-264

15. H-Sets for Non-Linear Constrained Approximation

    • M. Brannigan

    Pages 265-270

16. Operator Pade Approximants: Some ideas behind the theory and a numerical illustration

    • Annie A. H. Cuyt

    Pages 271-288

17. Harmonic Approximation

    • Myron Goldstein

    Pages 289-292

18. Best Harmonic L1 Approximation to Subharmonic Functions

    • M. Goldstein, W. Haussman, K. Jetter

    Pages 293-295

19. B-Splines on the Circle and Trigonometric B-Splines

    • T. N. T. Goodman, S. L. Lee

    Pages 297-325

20. On Reducing the Computational Error in the Successive Approximations Method

    • Francois B. Guénard

    Pages 327-338

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.

• approximation theory
• derivative
• extrema
• integral
• integral equation
• interpolation
• operator
• orthogonal polynomials

• Department of Mathematics and Statistics, Memorial University, St. John’s, Canada

  S. P. Singh, J. W. H. Burry, B. Watson

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