Titlebook: Numerische Methoden der Approximationstheorie; Band 2 L. Collatz,G. Meinardu Book 1975 Springer Basel AG 1975 Approximationstheorie.Differe

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A Method for the Numerical Computation of Best ,,-Approximations of Continuous Functions,hed an algorithm for the computation of such best approximations. However, Usow succeeded to prove the convergence of his algorithm only for conditions on . and on {....} which are fairly restrictiv and difficult to verify.

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Allgemeine Einschrittverfahren,ple for the construction of classical Runge-Kutta-procedures but also the possibility to put physical a-priori-knowledge about the solution into the procedure. Besides this, arbitrary order of accuracy may be reached without difficulties.

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,Zur Konstruktion einer Minimall?sung bei Linearer Simultanapproximation, .:B → . sei eine oberhalbstetige und .:B → . eine unterhalbstetige Funktion mit .(x) ≥ . für alle .. Wir suchen ein . ∈ ., das die Zahl. bezüglich . minimiert. Dabei verstehen wir unter ∥ ? ∥ die Tschebyscheff-Norm und setzen

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Allgemeine Einschrittverfahren,rature-formula. Then the right-hand-side of the differential equation has to be evaluated for some unknown values of the solution of the differential equation. This may be done by three various methods, called: recurrent quadratures, extrapolation, Taylor-series-expansions. Each of these possibiliti

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