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Lineare Gleichungssysteme

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Zusammenfassung

In diesem Abschnitt werden direkte Methoden zur Lösung von linearen Gleichungssystemen
$$Ax = b,\quad A = \left[ {\begin{array}{*{20}{c}} {{{a}_{{11}}} \cdots {{a}_{{1n}}}} \\ {.\quad \quad \quad .} \\ {.\quad \quad \quad .} \\ {.\quad \quad \quad .} \\ {{{a}_{{n1}}} \cdots {{a}_{{nn}}}} \\ \end{array} } \right],\quad b = \left[ {\begin{array}{*{20}{c}} {{{b}_{1}}} \\ . \\ . \\ . \\ {{{b}_{n}}} \\ \end{array} } \right]$$
dargestellt. Hier ist A eine gegebene n × n-Matrix, b ∈ ℝ n ein gegebener Vektor. Wir nehmen zusätzlich an, daß A und b reell sind, obwohl diese Einschränkung bei den meisten Verfahren unwesentlich ist. Im Gegensatz zu den iterativen Methoden (Kapitel 8), liefern die hier besprochenen direkten Verfahren die Lösung in endlich vielen Schritten, rundungsfehlerfreie Rechnung vorausgesetzt.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Institut für Angewandte Mathematik und StatistikUniversität WürzburgWürzburgDeutschland

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