Padé Approximants

Thoroughly updated, with material on multiseries approximants, circuit design, matrix Padé approximation and computational methods.

George A. Baker (Author), Peter Graves-Morris (Author)

9780521135092, Cambridge University Press

Paperback, published 11 March 2010

764 pages
23.4 x 15.6 x 3.8 cm, 1.1 kg

Review of the hardback: 'There can only be one conclusion: this book is indispensable to the researcher and the would-be researcher in the field of Padé approximation … one can only feel great admiration for the authors: they have done a splendid job incorporating all major developments in the theory and application of Padé approximation over the latest 15 years! Mathematika

The first edition of this book was reviewed in 1982 as 'the most extensive treatment of Padé approximants actually available'. This second edition has been thoroughly updated, with a substantial chapter on multiseries approximants. Applications to statistical mechanics and critical phenomena are extensively covered, and there are extended sections devoted to circuit design, matrix Pade approximation, and computational methods. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.

1. Introduction and definitions
2. Elementary developments
3. Padé approximants and numerical methods
4. Connection with continued fractions
5. Stieltjes series and Polya series
6. Convergence theory
7. Extensions of Padé approximants
8. Multiseries approximants
9. Connection with integral equations and quantum mechanics
10. Connection with numerical analysis
11. Connection with quantum field theory
Bibliography
Appendix: a FORTRAN program.

Subject Areas: Probability & statistics [PBT]