Overview

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(r) -1 r-x beziehungsweise r 1 P (x) (1. 5. b) ( ) J w(x) ~ dx .

Full Product Details

Author:   G. Hämmerlin ,  K.H. Hoffmann
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1985 ed.
Volume:   73
Weight:   0.690kg
ISBN:  

9783764316853

ISBN 10:   3764316853
Pages:   284
Publication Date:   01 January 1985
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Die Fehlernorm spezieller Gauss-Quadraturformeln.- Solving integral equations on surfaces in space.- An adaptive step size control for Volterra integral equations.- Concerning A(?)-stable mixed Volterra Runge-Kutta methods.- Constrained approximation techniques for solving integral equations.- On the numerical solution by collocation of Volterra integrodifferential equations with nonsmooth solutions.- Inclusion of regular and singular solutions of certain types of integral equations.- Two methods for solving the inverse scattering problem for time-harmonic acoustic waves.- Beyond superconvergence of collocation methods for Volterra integral equations of the first kind.- Optimal discrepancy principles for the Tikhonov regularization of integral equations of the first kind.- Spline-Galerkin method for solving some quantum mechanic integral equations.- Integral treatment of O.D.E with splines.- Product integration for weakly singular integral equations in ?m.- Stability results for discrete Volterra equations: Numerical experiments.- The design of acoustic torpedos.- On the condition number of boundary integral equations in acoustic scattering using combined double- and single-layer potentials.- Numerical solution of singular integral equations and an application to the theory of jet-flapped wings.- Tikhonov-Phillips regularization of the Radon Transform.- Numerical solution of a first kind Fredholm integral equation arising in electron-atom scattering.- Approximate solution of ill-posed equations: Arbitrarily slow convergence vs. superconvergence.- A unified analysis of discretization methods for Volterra-type equations.- Wiener-Hopf integral equations: Finite section approximation and projection methods..- Stability results for Abel equation.- Problems.

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