Constructive Methods for the Practical Treatment of Integral Equations: Proceedings of the Conference at the Mathematisches Forschungsinstitut Oberwolfach, June 24-30, 1984
G. Hammerlin,K.H. Hoffmann
Constructive Methods for the Practical Treatment of Integral Equations: Proceedings of the Conference at the Mathematisches Forschungsinstitut Oberwolfach, June 24-30, 1984
G. Hammerlin,K.H. Hoffmann
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O I 1 -1 durch die GauB-Quadraturformel Q I n n L w 0 f (x 0) * i=1 1 1 Sei Rn : = I - Q das Fehlerfunktional. n Izl1, Fur eine im Kreis Kr I Kr : = {z E a: holomorphe Funktion f, f(z) = L i=O sei f i i * = x . ( 1. 1) : = sup{ I a 0 I r i E:JN und R (qo) * O}, qo (x) o 1 n 1 1 In Xr := {f: f holomorph in Kr und Iflr < oo} ist I . I eine Seminorm. Das Fehlerfunktional Rn ist in r (X I* I r) stetig I und fUr II Rn II I r, gilt die Identitat 00 (1 . 2) L i=O Dieser Zugang zu ableitungsfreien Abschatzungen des Fehlerterms (1 * 3) geht auf Hammerlin [4] zurUck. 15 Erftillt die Gewichtsfunktion w eine der Bedingungen w (t ) w(t ) 1 2;;; (1. 4. a) w (-t ) w (-t ) 1 2 beziehungsweise w (t ) w(t ) 1 2 (1. 4. b) ~ w (-t ) w (-t ) 1 2 so gilt mit P (x) (X-X ) *. * (X-X ) ftir die Fehlernorm 1 n n r 1 Pn(x) (1. 5. a) –,-. . - J w (x) dx Pn® -1 r-x beziehungsweise r 1 P (x) (1. 5. b) ( ) J w(x) ~ dx .
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