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| Content Provider | Springer Nature Link |
|---|---|
| Author | Kowalski, Klaus |
| Copyright Year | 2012 |
| Abstract | 1974 wurden von Lorentz (The Birkhoff interpolation problem: new methods and results, Birkhäuser, Basel, 1974) erstmals Inzidenzmatrizen untersucht, die höchstens eine nichthermitesche Zeile enthalten, und von ihm als fasthermitesche Inzidenzmatrizen bezeichnet. Ziel der vorliegenden Arbeit ist die Vereinfachung der Untersuchung fasthermitescher Inzidenzmatrizen auf Freiheit, schwache und starke Unfreiheit durch Einführung sogenannter Koeffizientenpolynome $${P_{m}^g (E_{\bf n}^{\bf j})}$$ . Dies geschieht durch Satz 3.1. Die von uns betrachteten Koeffizientenpolynome $${P_{m}^g(E^{\bf j}_{\bf n})}$$ fasthermitescher Inzidenzmatrizen sind für m = 1 (bis auf das entgegengesetzte Vorzeichen des inneren Monoms X 1) identisch mit den 1978 von Drols (Drols in Zur Hermite–Birkhoff-Interpolation, 1978) (vgl. Drols in Math. Z. 172:179–194, 1980) eingeführten Koeffizientenpolynomen für spezielle dreizeilige fasthermitesche Inzidenzmatrizen, die er DMS-Inzidenzmatrizen nannte. Mit Satz 4.1 als Beispiel zeigen wir an einem Hauptsatz über fasthermitesche Inzidenzmatrizen, dass selbst ehemals komplexe und umfangreiche Beweise, die durch geschickte Überarbeitung bzgl. des Umfanges sowie Schwierigkeitsgrades reduziert wurden (vgl. (Drols in Zur Hermite–Birkhoff-Interpolation, 1978) (6.2) mit (Drols in Fasthermitesche Inzidenzmatrizen. Schriftenreihe des Fachbereichs Mathematik der Universität Duisburg Gesamthochschule, 1981) (1)), sich mittels der neuen Koeffizientenpolynome nochmals erheblich vereinfachen und verkürzen lassen. Satz 4.2 liefert als Anwendung von 4.1 ein neues (vgl. (Drols in Zur Hermite–Birkhoff-Interpolation, 1978); (Fasthermitesche Inzidenzmatrizen. Schriftenreihe des Fachbereichs Mathematik der Universität Duisburg Gesamthochschule, 1981) (1)); (Lorentz in The Birkhoff interpolation problem: new methods and results, Birkhäuser, Basel, 1974); (Lorentz in Birkhoff interpolation problem, 1975); (Lorentz in Birkhoff interpolation, Encyclopedia of Mathematics and its Applications, 19, Addison-Wesley, Reading, 1983) Kriterium f¨ur die starke Unfreiheit fasthermitescher Inzidenzmatrizen. |
| Ending Page | 414 |
| Page Count | 10 |
| Starting Page | 405 |
| File Format | |
| ISSN | 14226383 |
| e-ISSN | 14209012 |
| Journal | Results in Mathematics |
| Issue Number | 3 |
| Volume Number | 62 |
| Language | German |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2012-09-08 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Interpolation Approximation by polynomials Koeffizientenpolynome Mathematics Fasthermitesche Inzidenzmatrizen Hermite–Birkhoff-Interpolation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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