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A Course in Approximation Theory
 
Ward Cheney University of Texas at Austin, Austin, TX
Front Cover for A Course in Approximation Theory
Available Formats:
Hardcover ISBN: 978-0-8218-4798-5
Product Code: GSM/101
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN: 978-1-4704-1165-7
Product Code: GSM/101.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00
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Front Cover for A Course in Approximation Theory
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  • Front Cover for A Course in Approximation Theory
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A Course in Approximation Theory
Ward Cheney University of Texas at Austin, Austin, TX
Available Formats:
Hardcover ISBN:  978-0-8218-4798-5
Product Code:  GSM/101
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN:  978-1-4704-1165-7
Product Code:  GSM/101.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00
MAA Member Price: $105.30
AMS Member Price: $93.60
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1012000; 359 pp
    MSC: Primary 41;

    This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable.

    Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions.

    An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.

    Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-36224-9.

    Readership

    Graduate students and research mathematicians interested in approximation theory and applications.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introductory discussion of interpolation
    • Chapter 2. Linear interpolation operators
    • Chapter 3. Optimization of the Lagrange operator
    • Chapter 4. Multivariate polynomials
    • Chapter 5. Moving the nodes
    • Chapter 6. Projections
    • Chapter 7. Tensor-product interpolation
    • Chapter 8. The Boolean algebra of projections
    • Chapter 9. The Newton paradigm for interpolation
    • Chapter 10. The Lagrange paradigm for interpolation
    • Chapter 11. Interpolation by translates of a single function
    • Chapter 12. Positive definite functions
    • Chapter 13. Strictly positive definite functions
    • Chapter 14. Completely monotone functions
    • Chapter 15. The Schoenberg interpolation theorem
    • Chapter 16. The Micchelli interpolation theorem
    • Chapter 17. Positive definite functions on spheres
    • Chapter 18. Approximation by positive definite functions
    • Chapter 19. Approximation reconstruction of functions and tomography
    • Chapter 20. Approximation by convolution
    • Chapter 21. The good kernels
    • Chapter 22. Ridge functions
    • Chapter 23. Ridge function approximation via convolutions
    • Chapter 24. Density of ridge functions
    • Chapter 25. Artificial neural networks
    • Chapter 26. Chebyshev centers
    • Chapter 27. Optimal reconstruction of functions
    • Chapter 28. Algorithmic orthogonal projections
    • Chapter 29. Cardinal B-splines and the sinc function
    • Chapter 30. The Golomb-Weinberger theory
    • Chapter 31. Hilbert function spaces and reproducing kernels
    • Chapter 32. Spherical thin-plate splines
    • Chapter 33. Box splines
    • Chapter 34. Wavelets, I
    • Chapter 35. Wavelets II
    • Chapter 36. Quasi-interpolation
  • Reviews
     
     
    • Working through this book provides an opportunity to review and apply areas of mathematics learned elsewhere, as well as to learn entirely new topics.

      MAA Reviews
    • The textbook, a clear and concise work written by world-renowned experts in the field of approximation theory, will probe useful not only as a reference for professional mathematicians but also as a text for graduate students.

      Mathematical Reviews
  • Request Exam/Desk Copy
  • Request Review Copy
  • Get Permissions
Volume: 1012000; 359 pp
MSC: Primary 41;

This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable.

Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions.

An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.

Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-36224-9.

Readership

Graduate students and research mathematicians interested in approximation theory and applications.

  • Chapters
  • Chapter 1. Introductory discussion of interpolation
  • Chapter 2. Linear interpolation operators
  • Chapter 3. Optimization of the Lagrange operator
  • Chapter 4. Multivariate polynomials
  • Chapter 5. Moving the nodes
  • Chapter 6. Projections
  • Chapter 7. Tensor-product interpolation
  • Chapter 8. The Boolean algebra of projections
  • Chapter 9. The Newton paradigm for interpolation
  • Chapter 10. The Lagrange paradigm for interpolation
  • Chapter 11. Interpolation by translates of a single function
  • Chapter 12. Positive definite functions
  • Chapter 13. Strictly positive definite functions
  • Chapter 14. Completely monotone functions
  • Chapter 15. The Schoenberg interpolation theorem
  • Chapter 16. The Micchelli interpolation theorem
  • Chapter 17. Positive definite functions on spheres
  • Chapter 18. Approximation by positive definite functions
  • Chapter 19. Approximation reconstruction of functions and tomography
  • Chapter 20. Approximation by convolution
  • Chapter 21. The good kernels
  • Chapter 22. Ridge functions
  • Chapter 23. Ridge function approximation via convolutions
  • Chapter 24. Density of ridge functions
  • Chapter 25. Artificial neural networks
  • Chapter 26. Chebyshev centers
  • Chapter 27. Optimal reconstruction of functions
  • Chapter 28. Algorithmic orthogonal projections
  • Chapter 29. Cardinal B-splines and the sinc function
  • Chapter 30. The Golomb-Weinberger theory
  • Chapter 31. Hilbert function spaces and reproducing kernels
  • Chapter 32. Spherical thin-plate splines
  • Chapter 33. Box splines
  • Chapter 34. Wavelets, I
  • Chapter 35. Wavelets II
  • Chapter 36. Quasi-interpolation
  • Working through this book provides an opportunity to review and apply areas of mathematics learned elsewhere, as well as to learn entirely new topics.

    MAA Reviews
  • The textbook, a clear and concise work written by world-renowned experts in the field of approximation theory, will probe useful not only as a reference for professional mathematicians but also as a text for graduate students.

    Mathematical Reviews
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