An Introduction to the Approximation of Functions (Dover Books on Mathematics) by Theodore J. Rivlin (PDF)

Description

The needs of automatic digital computation have spurred an enormous revival of interest in methods of approximating continuous functions by functions that depend only on a finite number of parameters. This concise but wide-ranging text provides an introduction to some of the most significant of these methods, with particular emphasis on approximation by polynomials.Because approximation theory is an area of mathematics with important practical applications in computation, the author takes pains to discuss not only the theoretical underpinnings of many common algorithms, but to demonstrate the practical applications of the procedure. Thus, for each method of approximation studied, at least one algorithm leading to actual numerical approximation is described and traced to its present formulation.Apart from purely practical considerations, approximation theory is also a lively branch of mathematical analysis. Material in this book will be especially useful as additional reading in introductory courses in both mathematical and numerical analysis. It is particularly helpful in its coverage of a variety of approximation methods, including interpolation methods, and an introduction to splines, currently an area of great interest in approximation theory.Written for upper-level graduate students, this book presupposes a knowledge of advanced calculus and liner algebra, but the author has made a special effort to avoid some of the more sophisticated prerequisites in order to keep the topic within the grasp of the uninitiated. Abundant exercise material at the end of each chapter and an excellent bibliography contribute to the uniqueness and value of Dr. Rivlin’s book. As mathematical research continues to increase in complexity, the need to understand methods of approximation becomes even greater. This valuable text, one of the most accessible of its kind, represents an excellent introduction to this significant area of mathematical study.

User’s Reviews

Editorial Reviews: About the Author Theodore J. Rivlin was a Research Staff Member in the Department of Mathematical Sciences at IBM’s Thomas J. Watson Research Center in Yorktown Heights, New York.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐Dense & intense, and a very good summary of polynomial approximations.

⭐good

⭐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”.

⭐The book is terrific … I just want to know what a “dress reversal” is – as mentioned by a previous reviewer. Maybe I missed something!!

⭐und nach wie vor empfehlenswert. Rivlin schreibt klar und verständlich und auf den Punkt – d.h. kurz. Einziger Kritikpunkt: Einige Beweisschritte werden in Übungsaufgaben versteckt, zu denen es keine Lösungen gibt.Excellent

Keywords

Free Download An Introduction to the Approximation of Functions (Dover Books on Mathematics) in PDF format
An Introduction to the Approximation of Functions (Dover Books on Mathematics) PDF Free Download
Download An Introduction to the Approximation of Functions (Dover Books on Mathematics) 2010 PDF Free
An Introduction to the Approximation of Functions (Dover Books on Mathematics) 2010 PDF Free Download
Download An Introduction to the Approximation of Functions (Dover Books on Mathematics) PDF
Free Download Ebook An Introduction to the Approximation of Functions (Dover Books on Mathematics)