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Abstract: . We study the average case complexity of solving the Poisson equation \Deltau = f with zero boundary conditions on a smooth bounded region D ae R d . The right-hand side functions f are from F = C 2r (D), and the class F is endowed with a smooth isotropic Wiener measure that is a natural extension of the classical Wiener measure. We consider two problems: approximating the global solution u with respect to the L2 (D)-norm, and approximating a local solution which is the value of a... (Update)
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BibTeX entry: (Update)
K. Ritter and G. W. Wasilkowski, On the average case complexity of solving Poisson equations, Lectures in Applied Mathematics, 32, 677-687, 1996. http://citeseer.ist.psu.edu/ritter96average.html More
@incollection{ ritter96average,
author = "Ritter and Wasilkowski",
title = "On the Average Case Complexity of Solving Poisson Equations",
booktitle = "The Mathematics of Numerical Analysis: 1995 (25th) {AMS}-{SIAM} Summer Seminar in Applied Mathematics (Lectures in Applied Mathematics, Volume 32), American Mathematical Society",
editor = "Renegar and Shub and Smale",
year = "1996",
url = "citeseer.ist.psu.edu/ritter96average.html" }
Citations (may not include all citations):134 Information-Based Complexity (context) - Traub, Wasilkowski et al. - 1988
110 The Geometry of Random Fields (context) - Adler - 1981
49 A combination technique for the solution of sparse grid prob.. - Griebel, Schneider - 1992
42 Deterministic and Stochastic Error Bounds in Numerical Analy.. (context) - Novak - 1988
32 Explicit cost bounds of algorithms for multivariate tensor p.. - Wasilkowski, Wo'zniakowski - 1995
20 The Computational Complexity of Differential and Integral Eq.. (context) - Werschulz - 1991
17 Multivariate integration and approximation for random fields.. - Ritter, Wasilkowski et al. - 1995
16 On approximate calculation of integrals (context) - Bakhvalov - 1959
11 Average case complexity of linear multivariate problems: Par.. - Wo'zniakowski - 1992
10 Processus Stochastique et Mouvement Brownien (context) - L'evy - 1948
7 Information of varying cardinality (context) - Wasilkowski - 1986
5 approximation: average case setting with isotropic Wiener me.. (context) - Ritter, Wasilkowski et al. - 1996
4 On L'evy's Brownian motion with several-dimensional time (context) - Ciesielski - 1975
4 On some problems concerning Brownian motion in L'evy's sense (context) - Molchan - 1967
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