Padé approximants / George A. Baker, Jr., Peter Graves-Morris.

By:

Baker, George A. (George Allen), 1932- [author.]

Contributor(s):

Graves-Morris, P. R [author.]

Material type: Text

TextSeries: Encyclopedia of mathematics and its applications ; v. 59.Publisher: Cambridge [England] ; New York : Cambridge University Press, 1996Edition: Second editionDescription: 1 online resource (xiv, 746 pages) : illustrationsContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781107088573
1107088577
9780511959028
0511959028
9781107094758
1107094755

Subject(s): Genre/Form:

Additional physical formats: Print version:: Padé approximants.DDC classification:

515/.2432 23

LOC classification:

QC20.7.P3 B35 1996

Other classification:

31.49

Online resources:

EBSCOhost

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.

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.Summary: 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.

Holdings ( 1 )
Title notes ( 6 )

Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
eBook	e-Library	EBSCO Mathematics		Available

Total holds: 0

Includes bibliographical references (pages 695-740) and index.

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.

Description based on online resource; title from digital title page (viewed on March 15, 2021).

Master record variable field(s) change: 050, 082