Course in Approximation Theory

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $47.30
Usually ships in 1-2 business days
(Save 35%)
Other sellers (Hardcover)
  • All (3) from $47.30   
  • New (1) from $65.00   
  • Used (2) from $47.30   

Overview

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.

Read More Show Less

Editorial Reviews

Booknews
The central theme of the graduate textbook is the problem of interpolating data by smooth multivariable functions. Several chapters investigate interesting families of functions that can be employed in this task. The book then moves on to the consideration of methods for concocting approximations, such as by convolutions, by neural nets, or by interpolation at more and more points. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Read More Show Less

Product Details

  • ISBN-13: 9780821847985
  • Publisher: American Mathematical Society
  • Publication date: 1/13/2009
  • Series: Graduate Studies in Mathematics Series, #101
  • Edition description: New Edition
  • Pages: 359
  • Product dimensions: 6.40 (w) x 9.30 (h) x 0.70 (d)

Meet the Author

U of Leicester, U.K.
Read More Show Less

Table of Contents

Ch. 1 Introductory Discussion of Interpolation 1

Ch. 2 Linear Interpolation Operators 11

Ch. 3 Optimization of the Lagrange Operator 18

Ch. 4 Multivariate Polynomials 25

Ch. 5 Moving the Nodes 32

Ch. 6 Projections 39

Ch. 7 Tensor-Product Interpolation 46

Ch. 8 The Boolean Algebra of Projections 51

Ch. 9 The Newton Paradigm for Interpolation 57

Ch. 10 The Lagrange Paradigm for Interpolation 62

Ch. 11 Interpolation by Translates of a Single Function 71

Ch. 12 Positive Definite Functions 77

Ch. 13 Strictly Positive Definite Functions 87

Ch. 14 Completely Monotone Functions 94

Ch. 15 The Schoenberg Interpolation Theorem 101

Ch. 16 The Micchelli Interpolation Theorem 109

Ch. 17 Positive Definite Functions on Spheres 119

Ch. 18 Approximation by Positive Definite Functions 131

Ch. 19 Approximate Reconstruction of Functions and Tomography 141

Ch. 20 Approximation by Convolution 148

Ch. 21 The Good Kernels 157

Ch. 22 Ridge Functions 165

Ch. 23 Ridge Function Approximation via Convolutions 177

Ch. 24 Density of Ridge Functions 184

Ch. 25 Artificial Neural Networks 189

Ch. 26 Chebyshev Centers 197

Ch. 27 Optimal Reconstruction of Functions 202

Ch. 28 Algorithmic Orthogonal Projections 210

Ch. 29 Cardinal B-Splines and the Sinc Function 215

Ch. 30 The Golomb-Weinberger Theory 223

Ch. 31 Hilbert Function Spaces and Reproducing Kernels 232

Ch. 32 Spherical Thin-Plate Splines 246

Ch. 33 Box Splines 260

Ch. 34 Wavelets, I 272

Ch. 35 Wavelets, II 285

Ch. 36 Quasi-Interpolation 312

Bibliography 327

Index 355

Index of Symbols 359

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)