Padé approximants /:
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...
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| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1996.
|
| Ausgabe: | Second edition. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 59. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xiv, 746 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 695-740) and index. |
| ISBN: | 9781107088573 1107088577 9780511959028 0511959028 9781107094758 1107094755 0511530072 9780511530074 |
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| 245 | 1 | 0 | |a Padé approximants / |c George A. Baker, Jr., Peter Graves-Morris. |
| 250 | |a Second edition. | ||
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| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 520 | 8 | |a 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. | |
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Datensatz im Suchindex
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| author | Baker, George A. (George Allen), 1932- Graves-Morris, P. R. |
| author_GND | http://id.loc.gov/authorities/names/n81032271 http://id.loc.gov/authorities/names/n81035640 |
| author_facet | Baker, George A. (George Allen), 1932- Graves-Morris, P. R. |
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| 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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| dewey-raw | 515/.2432 |
| dewey-search | 515/.2432 |
| dewey-sort | 3515 42432 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition. |
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| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:39Z |
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| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Baker, George A. (George Allen), 1932- author. https://id.oclc.org/worldcat/entity/E39PCjCVJmDP39dyCT8rmWCBbm http://id.loc.gov/authorities/names/n81032271 Padé approximants / George A. Baker, Jr., Peter Graves-Morris. Second edition. Cambridge [England] ; New York : Cambridge University Press, 1996. 1 online resource (xiv, 746 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; volume 59 Includes bibliographical references (pages 695-740) and index. 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. 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. Online resource; title from digital title page (viewed on March 15, 2021). Padé approximant. http://id.loc.gov/authorities/subjects/sh85096553 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Approximants de Padé. Physique mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical physics fast Padé approximant fast Padé-benaderingen. gtt Padé, Approximants de. ram Physique mathématique. ram Graves-Morris, P. R., author. http://id.loc.gov/authorities/names/n81035640 Print version: Baker, George A. (George Allen), 1932- Padé approximants. Second edition 0521450071 (DLC) 94048506 (OCoLC)31776481 Encyclopedia of mathematics and its applications ; v. 59. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569344 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569344 Volltext |
| spellingShingle | Baker, George A. (George Allen), 1932- Graves-Morris, P. R. Padé approximants / Encyclopedia of mathematics and its applications ; 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. Padé approximant. http://id.loc.gov/authorities/subjects/sh85096553 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Approximants de Padé. Physique mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical physics fast Padé approximant fast Padé-benaderingen. gtt Padé, Approximants de. ram Physique mathématique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85096553 http://id.loc.gov/authorities/subjects/sh85082129 |
| title | Padé approximants / |
| title_auth | Padé approximants / |
| title_exact_search | Padé approximants / |
| title_full | Padé approximants / George A. Baker, Jr., Peter Graves-Morris. |
| title_fullStr | Padé approximants / George A. Baker, Jr., Peter Graves-Morris. |
| title_full_unstemmed | Padé approximants / George A. Baker, Jr., Peter Graves-Morris. |
| title_short | Padé approximants / |
| title_sort | pade approximants |
| topic | Padé approximant. http://id.loc.gov/authorities/subjects/sh85096553 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Approximants de Padé. Physique mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical physics fast Padé approximant fast Padé-benaderingen. gtt Padé, Approximants de. ram Physique mathématique. ram |
| topic_facet | Padé approximant. Mathematical physics. Approximants de Padé. Physique mathématique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Mathematical physics Padé approximant Padé-benaderingen. Padé, Approximants de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569344 |
| work_keys_str_mv | AT bakergeorgea padeapproximants AT gravesmorrispr padeapproximants |