Laurent Series and their Padé Approximations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1987
|
| Schriftenreihe: | Operator Theory: Advances and Applications
27 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity |
| Beschreibung: | 1 Online-Ressource (XI, 276 p) |
| ISBN: | 9783034893060 9783034899888 |
| DOI: | 10.1007/978-3-0348-9306-0 |
Internformat
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| 500 | |a The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity | ||
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Datensatz im Suchindex
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| author | Bultheel, Adhemar |
| author_facet | Bultheel, Adhemar |
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| author_sort | Bultheel, Adhemar |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV042422345 |
| classification_rvk | SK 470 SK 620 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863791878 (DE-599)BVBBV042422345 |
| dewey-full | 50 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 050 - General serial publications |
| dewey-raw | 50 |
| dewey-search | 50 |
| dewey-sort | 250 |
| dewey-tens | 050 - General serial publications |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| doi_str_mv | 10.1007/978-3-0348-9306-0 |
| format | Electronic eBook |
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| id | DE-604.BV042422345 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783034893060 9783034899888 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857762 |
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| physical | 1 Online-Ressource (XI, 276 p) |
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| spelling | Bultheel, Adhemar Verfasser aut Laurent Series and their Padé Approximations by Adhemar Bultheel Basel Birkhäuser Basel 1987 1 Online-Ressource (XI, 276 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 27 The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity Science (General) Science, general Naturwissenschaft Laurent-Entwicklung (DE-588)4224176-5 gnd rswk-swf Laurent-Reihe (DE-588)4192933-0 gnd rswk-swf Padé-Näherung (DE-588)4173060-4 gnd rswk-swf Laurent-Reihe (DE-588)4192933-0 s Padé-Näherung (DE-588)4173060-4 s DE-604 Laurent-Entwicklung (DE-588)4224176-5 s Erscheint auch als Druck-Ausgabe 3-7643-1940-2 https://doi.org/10.1007/978-3-0348-9306-0 Verlag Volltext |
| spellingShingle | Bultheel, Adhemar Laurent Series and their Padé Approximations Science (General) Science, general Naturwissenschaft Laurent-Entwicklung (DE-588)4224176-5 gnd Laurent-Reihe (DE-588)4192933-0 gnd Padé-Näherung (DE-588)4173060-4 gnd |
| subject_GND | (DE-588)4224176-5 (DE-588)4192933-0 (DE-588)4173060-4 |
| title | Laurent Series and their Padé Approximations |
| title_auth | Laurent Series and their Padé Approximations |
| title_exact_search | Laurent Series and their Padé Approximations |
| title_full | Laurent Series and their Padé Approximations by Adhemar Bultheel |
| title_fullStr | Laurent Series and their Padé Approximations by Adhemar Bultheel |
| title_full_unstemmed | Laurent Series and their Padé Approximations by Adhemar Bultheel |
| title_short | Laurent Series and their Padé Approximations |
| title_sort | laurent series and their pade approximations |
| topic | Science (General) Science, general Naturwissenschaft Laurent-Entwicklung (DE-588)4224176-5 gnd Laurent-Reihe (DE-588)4192933-0 gnd Padé-Näherung (DE-588)4173060-4 gnd |
| topic_facet | Science (General) Science, general Naturwissenschaft Laurent-Entwicklung Laurent-Reihe Padé-Näherung |
| url | https://doi.org/10.1007/978-3-0348-9306-0 |
| work_keys_str_mv | AT bultheeladhemar laurentseriesandtheirpadeapproximations |