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Constructive Methods for the Practical Treatment of Integral Equations : Proceedings of the Conference Mathematisches Forschungsinstitut Oberwolfach, June 24-30, 1984

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概要 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 .続きを見る
目次 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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登録日 2020.06.27
更新日 2020.06.28