This graduate-level text offers a concise but wide-ranging introduction to methods of approximating continuous functions by functions depending only on a finite number of parameters. It places particular emphasis on approximation by polynomials and not only discusses the theoretical underpinnings of many common algorithms but also demonstrates their practical applications. 1969 edition.
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Most Helpful Customer Reviews
11 of 12 people found the following review helpful:
5.0 out of 5 stars
Not a good FIRST book on approximation theory,
By UNPINGCO (Los Angeles, CA) - See all my reviews
This review is from: An Introduction to the Approximation of Functions (Dover Books on Mathematics) (Paperback)
This is a good introduction to approximation theory, but not a good first book on approximation theory. The standard topics are covered: uniform approximation, least squares approximation, polynomial and spline interpolation, and approximation and interpolation by rational functions. Each of these topics deals with real valued functions of a real variable.This book suits someone who has a good basic understanding of functional analysis: compact sets, uniform continuity, basic operator theory. Having said that, this book is actually quite good because instead of just listing the standard results accompanied with the tightest proofs, the author usually take a motivating approach to each of the results. He often starts out with a certain line of reasoning, demonstrates the resulting complications, and then picks up another line of reasoning that makes the result more apparent. This is very instructive because it gives you an insight to the "dress reversal" instead of just the "performance".
3 of 3 people found the following review helpful:
5.0 out of 5 stars
Clear, concise, and complete,
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Amazon Verified Purchase(What's this?)
This review is from: An Introduction to the Approximation of Functions (Dover Books on Mathematics) (Paperback)
This is a great book for getting started with approximation theory. All you really need to do this book is a decent background in calculus and linear algebra: all the functional analysis and other tools you need are provided in the book. The only drawback to the book is that it's out-of-date and no longer reflects current research, but it does a great job in covering all the basics you'll need to understand the new, advanced stuff when you go looking for it in other books and journals. Still, this book is indispensable and I would recommend it over every other book I've seen in the field if you're new to approximation theory.
3 of 8 people found the following review helpful:
4.0 out of 5 stars
Great book ...,
By G. Cantor "Base three" (Mill Valley, CA USA) - See all my reviews
Amazon Verified Purchase(What's this?)
This review is from: An Introduction to the Approximation of Functions (Dover Books on Mathematics) (Paperback)
The book is terrific ... I just want to know what a "dress reversal" is - as mentioned by a previous reviewer. Maybe I missed something!!
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Citations (learn more)
26
books
cite this book:
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- Advanced Calculus with Applications in Statistics by André I. Khuri on page 442, and Back Matter
- Advanced Calculus with Applications in Statistics (Wiley Series in Probability and Statistics) by André I. Khuri on page 433, and Back Matter
- Interpolation and Approximation by Polynomials by George M. Phillips in Back Matter
- On L1-Approximation (Cambridge Tracts in Mathematics) by Allan M. Pinkus in Back Matter
- Simulation of Communication Systems: Modeling, Methodology and Techniques (Information Technology: Transmission, Processing and Storage) by Michel C. Jeruchim on page 131
See all 26 books citing this book
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