Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
maximize
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Literatur

1
K. I. Babenko, Approximation by trigonometric polynomials in a certain class of periodic functions of several variables, Dokl. Akad. Nauk SSSR 132 (1960), 672-675.

2
H.-J. Bungartz, Dünne Gitter und deren Anwendung bei der adaptiven Lösung der dreidimensionalen Poisson-Gleichung, Dissertation, Inst. für Informatik, TU München, 1992.

3
H.-J. Bungartz, M. Griebel, A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives, J. Complexity 15 (1999), 167-199.

4
P. L. Butzer, K. Scherer, Approximationsprozesse und Interpolationsmethoden, Bibliographisches Institut Mannheim, Mannheim, 1968.

5
K. Cios, W. Pedrycz, R. Swniarski, Data Mining methods for Knowledge Discovery, Kluwer Academic Publishers, Boston, 1998.

6
W. Dahmen, A. Kunoth, Multilevel preconditioning, Numer. Math. 63 (1992), 315-344.

7
U. Fayyad, G. Piatetsky-Shapiro, P. Smyth, R. Uthurusamy, editors, Advances in Knowledge Discovery and Data Mining, AAAI/MIT-Press, 1996.

8
F. Girosi, An Equivalence Between Sparse Approximation and Support Vector Machines, Neural Computation 10(6) (1998), 1455-1480.

9
F. Girosi, M. Jones, T. Poggio, Priors, Stabilizers and Basis Functions: from regularization to radial, tensor and additive splines, A.I. Memo No. 1430, Artificial Intelligence Laboratory, MIT, 1993.

10
F. Girosi, M. Jones, T. Poggio, Regularization Theory and Neural Network Architecture, Neural Computations 7 (1995), 219-265.

11
M. Griebel, The combination technique for the sparse grid solution of PDEs on multiprocessor machines, Parallel Processing Letters 2(1) (1992), 61-70.

12
M. Griebel, W. Huber, U. Rüde, T. Störtkuhl, The combination technique for parallel sparse-grid-preconditioning and -solution of PDEs on multiprocessor machines and workstation networks, in L. Bouge, M. Cosnard, Y. Robert and D. Trystram (eds.), Lecture Notes in Computer Science 634, Parallel Processing: CONPAR92-VAPP V, 217-228, Springer Verlag, 1992.

13
M. Griebel, S. Knapek, Optimized approximation spaces for operator equations, SFB-256 Bericht Nr. 568, Universität Bonn, 1998.

14
M. Griebel, M. Schneider, C. Zenger, A combination technique for the solution of sparse grid problems, in Iterative Methods in Linear Algebra, P. de Groen and R. Beauwens (eds.), Elsevier, Amsterdam, 1992, 263-281.

15
D. Michie, D.J. Spiegelhalter, C.C. Taylor, Machine Learning, Neural and Statistical Classification, Ellis Horwood, N.Y., 1994.

16
S. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Dokl. Akad. Nauk SSSR 4 (1963), 240-243.

17
V. N. Temlyakov, Approximation of functions with bounded mixed derivative, Proceedings of the Steklov Institute of Mathematics 1 (1989).

18
V. Vapnik, The Nature of Statistical Learning Theory, Springer, N.Y. 1995.

19
R. Verführt, A posteriori error estimates and adaptive mesh refinement techniques, J. Comput. and Appl. Math. 50 (1994), 67-83.

20
C. Zenger, Sparse grids, Parallel Algorithms for Partial Differential Equations, Notes on Num. Fluid Mech. 31, W. Hackbusch (ed.), Vieweg, Braunschweig, 1991.



Jochen Garcke
2000-12-14