Monotone Einschließung von Inversen positiver Elemente durch Verfahren vom Schulz-Typ |
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| Authors: | Prof Dr J W Schmidt |
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| Affiliation: | 1. Sektion Mathematik, Technische Universit?t Dresden, Mommsenstra?e 13, DDR-8027, Dresden, Deutsche Demokratische Republik
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| Abstract: | The conditional iterationx n+1 =sup (x n ,x n +x n (e?ax n )),y n?1 =inf (y n ,x n +y n (e?ax n )) generating sequences (x n ) and (y n ) is considered in partially ordered spaces. Under certain conditions it is shown, that the inversea ?1 of a positive elementa≧0 is monotonously enclosed in the sensex n ≦x n+1 ≦a ?1 ≦y n+1 ≦y n and that (x n ) and (y n ) converge toa ?1 quadratically. |
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