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Lineare Gleichungssysteme

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Numerische Mathematik 1

Part of the book series: Springer-Lehrbuch ((SLB))

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Zusammenfassung

In diesem Abschnitt werden direkte Methoden zur Lösung von linearen Gleichungssystemen

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiaadI % hacqGH9aqpcaWGIbGaaiilaiaaysW7caWGbbGaeyypa0ZaamWaaeaa % faqabeqbcaaaaeaacaWGHbWaaSbaaSqaaiaaigdacaaIXaaabeaaki % aac6cacaGGUaGaaiOlaaqaaiaadggadaWgaaWcbaGaaGymaiaad6ga % aeqaaaGcbaGaaiOlaaqaaiaac6caaeaacaGGUaaabaGaaiOlaaqaai % aac6caaeaacaGGUaaabaGaamyyamaaBaaaleaacaWGUbGaaGymaaqa % baGccaGGUaGaaiOlaiaac6caaeaacaWGHbWaaSbaaSqaaiaad6gaca % WGUbaabeaaaaaakiaawUfacaGLDbaacaGGSaGaaGjbVlaadkgacqGH % 9aqpdaWadaqaauaabeqafeaaaaqaaiaadkgadaWgaaWcbaGaaGymaa % qabaaakeaacaGGUaaabaGaaiOlaaqaaiaac6caaeaacaWGIbWaaSba % aSqaaiaad6gaaeqaaaaaaOGaay5waiaaw2faaaaa!5F65!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$Ax = b,\;A = \left[ {\begin{array}{*{20}{c}} {{a_{11}}...}&{{a_{1n}}} \\ .&. \\ .&. \\ .&. \\ {{a_{n1}}...}&{{a_{nn}}} \end{array}} \right],\;b = \left[ {\begin{array}{*{20}{c}} {{b_1}} \\ . \\ . \\ . \\ {{b_n}}\end{array}} \right]$$

dargestellt. Hier ist A eine gegebene n × n-Matrix, b 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, rundungsfehlerfreie Rechnung vorausgesetzt, in endlich vielen Schritten.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, 8700, Würzburg, Deutschland

    Prof. Dr. Josef Stoer

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  1. Prof. Dr. Josef Stoer
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© 1989 Springer-Verlag Berlin Heidelberg

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Stoer, J. (1989). Lineare Gleichungssysteme. In: Numerische Mathematik 1. Springer-Lehrbuch. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09024-4_4

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  • DOI: https://doi.org/10.1007/978-3-662-09024-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51481-7

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