Quantitative Approximation
eBook - PDF

Quantitative Approximation

Proceedings of a Symposium on Quantitative Approximation Held in Bonn, West Germany, August 20-24, 1979

  1. 336 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Quantitative Approximation

Proceedings of a Symposium on Quantitative Approximation Held in Bonn, West Germany, August 20-24, 1979

Book details
Table of contents
Citations

About This Book

Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses spline approximation with the most emphasis on multivariate and knot independent questions. Organized into 26 chapters, this book begins with an overview of the inequality for the sharp function in terms of the maximal rearrangement. This text then examines the best co-approximation in a Hilbert space wherein the existence ad uniqueness sets are the closed flats. Other chapters consider the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots. This book discusses as well the relationship between the structural properties of a function and its degree of approximation by rational functions. The final chapter deals with the problem of existence of continuous selections for metric projections and provides a solution for this problem. This book is a valuable resource for mathematicians.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483265124
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Front Cover
  2. Quantitative Approximation
  3. Copyright Page
  4. Table of Contents
  5. Contributors
  6. Preface
  7. CHAPTER 1. ON AN INEQUALITY FOR THE SHARP FUNCTION
  8. CHAPTER 2. ON THE BEST CO-APPROXIMATION IN A HILBERT SPACE
  9. CHAPTER 3. WHAT IS THE MAIN DIAGONAL OF A BIINFINITE BAND MATRIX ?
  10. CHAPTER 4. RATIONAL APPROXIMATION AND EXOTIC LIPSCHITZ SPACES
  11. CHAPTER 5. SOME MATHEMATICAL PROPERTIES OF EMPIRICALGIBBS FUNCTIONS
  12. CHAPTER 6. MULTIVARIATE INTERPOLATION AND THE RADON TRANSFORM,PART II: SOME FURTHER EXAMPLES
  13. CHAPTER 7. LACUNARY TRIGONOMETRIC INTERPOLATION ON EQUIDISTANT NODES
  14. CHAPTER 8. MONOTONE APPROXIMATION BY SPLINE FUNCTIONS
  15. CHAPTER 9. APPROXIMATION BY SMOOTH MULTIVARIATE SPLINES ONNON-UNI FORM GRIDS
  16. CHAPTER 10. APPROXIMATION BY SMALL RANK TENSOR PRODUCTS OF SPLINES
  17. CHAPTER 11. VARIABLE KNOT, VARIABLE DEGREE SPLINE APPROXIMATION TO Xβ
  18. CHAPTER 12. ON SHARP NECESSARY CONDITIONS FOR RADIALFOURIER MULTIPLIERS
  19. CHAPTER 13. APPROXIMATING BIVARIATE FUNCTIONS AND MATRICESBY NOMOGRAPHIC FUNCTIONS
  20. CHAPTER 14. L∞ -BOUNDS OF L2-- PROJECTIONS ON SPLINES
  21. CHAPTER 15. DIAMETERS OF CLASSES OF SMOOTH FUNCTIONS
  22. CHAPTER 16. ON ESTIMATES OF DIAMETERS
  23. CHAPTER 17. BOUNDS FOR THE ERROR IN TRIGONOMETRIC HERMITE INTERPOLATION
  24. CHAPTER 18. BIRKHOFF INTERPOLATION: SOME APPLICATIONS OF COALESCENCE
  25. CHAPTER 19. n-WIDTHS OF OCTAHEDRA
  26. CHAPTER 20. THE APPROXIMATION OF MULTIPLE INTEGRALS BY USING INTERPOLATORY CUBATURE FORMULAE
  27. CHAPTER 21. INTERPOLATORY CUBATURE FORMULAE AND REAL IDEALS
  28. CHAPTER 22. STRONG UNIQUENESS OF BEST APPROXIMATIONS AND WEAK CHEBYSHEV SYSTEMS
  29. CHAPTER 23. ON THE CONNECTION BETWEEN RATIONAL UNIFORM APPROXIMATION AND POLYNOMIAL LP APPROXIMATION OF FUNCTIONS
  30. CHAPTER 24. BEST CHEBYSHEV APPROXIMATION BY SMOOTH FUNCTIONS
  31. CHAPTER 25. APPROXIMATIONS IN THE HARDY SPACE H1 (D) WITH RESPECT TO THE NORM TOPOLOGY
  32. CHAPTER 26. CONTINUOUS SELECTIONS FOR METRIC PROJECTIONS
  33. PROBLEMS