Padé approximants
by Baker, George A., (George Allen)
The Pade approximant of a given power series is a rational function of numerator degree L and denominator degree M whose power series agrees with the given one up to degree L + M inclusively. A collection of Pade approximants formed by using a suitable set of values of L and M often provides a means of obtaining information about the function outside its circle of convergence, and of more rapidly evaluating the function within its circle of convergence. Applications of these ideas in physics, c…
Read More ↓Title Statements
- Full title :Padé approximants / George A. Baker, Jr., Peter Graves-Morris.
Summary
The Pade approximant of a given power series is a rational function of numerator degree L and denominator degree M whose power series agrees with the given one up to degree L + M inclusively. A collection of Pade approximants formed by using a suitable set of values of L and M often provides a means of obtaining information about the function outside its circle of convergence, and of more rapidly evaluating the function within its circle of convergence. Applications of these ideas in physics, chemistry, electrical engineering, and other areas have led to a large number of generalizations of Pade approximants that are tailor-made for specific applications. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, computational methods, and integral and algebraic approximants.
The book is written with a smooth progression from elementary ideas to some of the frontiers of research in approximation theory. Its main purpose is to make the various techniques described accessible to scientists, engineers, and other researchers who may wish to use them, while also presenting the rigorous mathematical theory.
Edition Statements
- Publication Date:1996.
- Edition:2nd ed
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge [England]
- Language:eng
- Publication Date:1996.
The Physical Object
- Description:xiv, 746 pages : : illustrations ; : 25 cm.
Edition Identifiers
- ISBN:0521450071, 9780521450072
- oclc:ocm31776481
- LC Classification:QA165
- Dewey Decimal:515/.2432
Table of Contents
1. Introduction and definitions -- 2. Elementary developments -- 3. Pade approximants and numerical methods -- 4. Connection with continued fractions -- 5. Stieltjes series and Polya series -- 6. Convergence theory -- 7. Extensions of Pade approximations -- 8. Multiseries approximants -- 9. Connection with integral equations and quantum mechanics -- 10. Connection with numerical analysis -- 11. Connection with quantum field theory -- Appendix: A FORTRAN FUNCTION.
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