Geodesic
Zrychlování konvergence lineárních iteračních procesů v Banachových prostorech
Applications of Mathematics, Tome 11 (1966) no. 4, pp. 266-270
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The convergence of the sequence $x_{n+1}=Ax_n+b$ to $(l-A)^{-1}b$ (where $x_n, b$ are vectors in Banach space, $A$ is a bounded linear operator with bounded $(l-A)^{-1}$) can be accelerated by constructing certain linear combinations of several ordinary successive approximations. A sufficient condition is that the spectrum of $A$ decompose into a finite set and a subset of a sufficiently small neighborhood of zero (e. g., $A$ is compact).
The convergence of the sequence $x_{n+1}=Ax_n+b$ to $(l-A)^{-1}b$ (where $x_n, b$ are vectors in Banach space, $A$ is a bounded linear operator with bounded $(l-A)^{-1}$) can be accelerated by constructing certain linear combinations of several ordinary successive approximations. A sufficient condition is that the spectrum of $A$ decompose into a finite set and a subset of a sufficiently small neighborhood of zero (e. g., $A$ is compact).
DOI : 10.21136/AM.1966.103028
Classification : 65.10
Mots-clés : numerical analysis 
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     title = {Zrychlov\'an{\'\i} konvergence line\'arn{\'\i}ch itera\v{c}n{\'\i}ch proces\r{u} v {Banachov\'ych} prostorech},
     journal = {Applications of Mathematics},
     pages = {266--270},
     year = {1966},
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Kovářík, Zdislav. Zrychlování konvergence lineárních iteračních procesů v Banachových prostorech. Applications of Mathematics, Tome 11 (1966) no. 4, pp. 266-270. doi: 10.21136/AM.1966.103028

[1] D. K. Faddějev V. N. Faddějevová: Numerické metody lineární algebry. SNTL, Praha 1964 (překlad z ruštiny).

[2] И. С. Березин H. П. Жидков: Методы вычислений, т. II. ФИЗМАТГИЗ, Москва 1962. | Zbl

[3] H. Данфорд, Дж. Шварц: Линейные операторы. (общая теория); ИИЛ, Москва 1962 (перевод с английского). | Zbl

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