Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
wavelet compression of operators; random data; Monte-Carlo method; wavelet finite element method
wavelet compression of operators; random data; Monte-Carlo method; wavelet finite element method
Summary:
References:
[1] I. Babuška: On randomized solution of Laplace’s equation. Čas. Pěst. Mat. 86 (1961), 269–276.
[2] I. Babuška: Error-bounds for finite element method. Numer. Math. 16 (1971), 322–333. MR 0288971
[3] I. Babuška, R. Tempone, and G. Zouraris: Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42 (2004), 800–825. MR 2084236
[4] V. I. Bogachev: Gaussian Measures. AMS Mathematical Surveys and Monographs Vol. 62. AMS, Providence, 1998. MR 1642391
[5] L. Breiman: Probability. Addison-Wesley, Reading, 1968. MR 0229267 | Zbl 0174.48801
[6] W. A. Light, E. W. Cheney: Approximation Theory in Tensor Product Spaces. Lecture Notes in Mathematics Vol. 1169. Springer-Verlag, Berlin, 1985. MR 0817984
[7] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. Elsevier Publ. North Holland, Amsterdam, 1978. MR 0520174 | Zbl 0383.65058
[8] M. Dahmen, H. Harbrecht, and R. Schneider: Compression techniques for boundary integral equations—optimal complexity estimates. SIAM J. Numer. Anal. 43 (2006), 2251–2271. MR 2206435
[9] W. Dahmen, R. Stevenson: Element-by-element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal. 37 (1999), 319–352. MR 1742747
[10] S. C. Eisenstat, H. C. Elman, M. H. Schultz: Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20 (1983), 345–357. MR 0694523
[11] M. Griebel, P. Oswald, T. Schiekofer: Sparse grids for boundary integral equations. Numer. Math. 83 (1999), 279–312. MR 1712687
[12] S. Hildebrandt, N. Wienholtz: Constructive proofs of representation theorems in separable Hilbert space. Commun. Pure Appl. Math. 17 (1964), 369–373. MR 0166608
[13] G. C. Hsiao, W. L. Wendland: A finite element method for some integral equations of the first kind. J. Math. Anal. Appl. 58 (1977), 449–481. MR 0461963
[14] S. Janson: Gaussian Hilbert Spaces. Cambridge University Press, Cambridge, 1997. MR 1474726 | Zbl 0887.60009
[15] S. Larsen: Numerical analysis of elliptic partial differential equations with stochastic input data. Doctoral Dissertation, Univ. of Maryland, 1985.
[16] M. Ledoux, M. Talagrand: Probability in Banach Spaces. Isoperimetry and Processes. Springer-Verlag, Berlin, 1991. MR 1102015
[17] P. Malliavin: Stochastic Analysis. Springer-Verlag, Berlin, 1997. MR 1450093 | Zbl 0878.60001
[18] W. McLean: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, 2000. MR 1742312 | Zbl 0948.35001
[19] J. C. Nédélec, J. P. Planchard: Une méthode variationelle d’éléments finis pour la résolution numérique d’un problème extérieur dans $\mathbb{R}^3$. RAIRO Anal. Numér. 7 (1973), 105–129. MR 0424022
[20] G. Schmidlin, C. Lage, and C. Schwab: Rapid solution of first kind boundary integral equations in $\mathbb{R}^3$. Eng. Anal. Bound. Elem. 27 (2003), 469–490.
[21] T. von Petersdorff, C. Schwab: Wavelet approximations for first kind boundary integral equations in polygons. Numer. Math. 74 (1996), 479–516. MR 1414419
[22] T. von Petersdorff, C. Schwab: Numerical solution of parabolic equations in high dimensions. M2AN, Math. Model. Numer. Anal. 38 (2004), 93–127. MR 2073932
[23] R. Schneider: Multiskalen- und Wavelet-Matrixkompression. Advances in Numerical Mathematics. Teubner, Stuttgart, 1998. MR 1623209
[24] C. Schwab, R. A. Todor: Sparse finite elements for elliptic problems with stochastic loading. Numer. Math. 95 (2003), 707–734. MR 2013125
[25] C. Schwab, R. A. Todor: Sparse finite elements for stochastic elliptic problems—higher order moments. Computing 71 (2003), 43–63. MR 2009650
[26] S. A. Smolyak: Quadrature and interpolation formulas for tensor products of certain classes of functions. Sov. Math. Dokl. 4 (1963), 240–243. Zbl 0202.39901
[27] V. N. Temlyakov: Approximation of Periodic Functions. Nova Science Publ., New York, 1994. MR 1373654
[28] G. W. Wasilkowski, H. Wozniakowski: Explicit cost bounds of algorithms for multivariate tensor product problems. J. Complexity 11 (1995), 1–56. MR 1319049
[29] N. Wiener: The homogeneous Chaos. Amer. J. Math. 60 (1938), 987–936. MR 1507356 | Zbl 0019.35406
Search
Partner of
