Exact Constants in Approximation Theory
eBook - PDF

Exact Constants in Approximation Theory

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Exact Constants in Approximation Theory

About this book

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.

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Yes, you can access Exact Constants in Approximation Theory by N. Korneichuk, K. Ivanov in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half Title
  3. Series Page
  4. Title
  5. Copyright
  6. CONTENTS
  7. PREFACE
  8. LIST OF MOST IMPORTANT NOTATION
  9. 1 Best approximation and duality in extremal problems
  10. 2 Polynomials and spline functions as approximating tools
  11. 3 Comparison theorems and inequalities for the norms of functions and their derivatives
  12. 4 Polynomial approximation of classes of functions with bounded rth derivative in Lp
  13. 5 Spline approximation of classes of functions with a bounded rth derivative
  14. 6 Exact constants in Jackson inequalities
  15. 7 Approximation of classes of functions determined by modulus of continuity
  16. 8 N-widths of functional classes and closely related extremal problems
  17. APPENDIX
  18. REFERENCES
  19. INDEX OF NOTATION
  20. INDEX