Numerische Berechnung Von Benachbarten Inversen Matrizen Und Linearen Gleichungssystemen
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Die numerische Behandlung von Matrizen gewinnt zunehmend Bedeutung in einer Vielzahl von Wissensgebieten; insbesondere tritt häuftg die Frage auf, wie sich Än- derungen an Matrizen auf die Inverse der Matrix auswirken. Als Operationen kom- men Addition, Ränderung und Reduktion von Matrizen in Frage. Solche Fragestel- lungen sind von besonderem Interesse, z. B. bei der Lösung von Gleichungssystemen, wenn man die Eingabedaten im oben angegebenen Sinne ändert und eine Neuberech- nung des gesamten Systems wegen des hohen Rechenaufwandes vermeiden möchte, wobei vor allem wirtschaftliche Erwägungen eine Rolle spielen. Das Problem ist bis- her nicht unter diesem allgemeinen Gesichtspunkt untersucht worden. Au erdem dürfte es sich um die erste zusammenfassende Darstellung handeln, die die Bedürf- nisse der Datenverarbeitung berücksichtigt. So werden zu den wichtigsten Verfahren getestete ALGOL-Prozeduren angegeben. Zu jedem der Verfahren sind numerische Beispiele angefUhrt, so da auch Leser, die sich nur sehr oberflächlich in der Matrizen- rechnung auskennen, daraus Gewinn ziehen können. Für das vertiefte Studium weiterer Einzelheiten gtbt das ausführliche Uteraturver- zeichnis eine gute Hilfestellung. Der Verfasser hat sich bemüht, den historischen Werdegang der einzelnen Formeln zu verfolgen, die sehr verstreut in der mathemati- schen literatur auftauchen. Es ist sehr zu begrü en, da versucht wurde, alle diese Formeln auf eine gemeinsame Wurzel zurückzuführen und man möchte hoffen, da sich weitere mathematische Untersuchungen mit diesen Fragestellungen beschäftigbn, die für die Praxis von gro er Bedeutung sein können, da der Rechenaufwand oft nicht unbeträchtlich gesenkt werden kann, wie man aus den im Text angegebenen Zusammenstellungen des Aufwands an Multiplikationen entnehmen kann.
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