In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.
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An Adaptive Sparse Grid Approach for Time Series Prediction |
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1 | (30) |
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Efficient Analysis of High Dimensional Data in Tensor Formats |
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31 | (26) |
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Sparse Grids in a Nutshell |
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57 | (24) |
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Intraday Foreign Exchange Rate Forecasting Using Sparse Grids |
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81 | (26) |
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Dimension- and Time-Adaptive Multilevel Monte Carlo Methods |
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107 | (14) |
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An Efficient Sparse Grid Galerkin Approach for the Numerical Valuation of Basket Options Under Kou's Jump-Diffusion Model |
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121 | (30) |
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The Use of Sparse Grid Approximation for the r-Term Tensor Representation |
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151 | (10) |
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On Multilevel Quadrature for Elliptic Stochastic Partial Differential Equations |
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161 | (20) |
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Local and Dimension Adaptive Stochastic Collocation for Uncertainty Quantification |
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181 | (24) |
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The Combination Technique for the Initial Value Problem in Linear Gyrokinetics |
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205 | (18) |
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Model Reduction with the Reduced Basis Method and Sparse Grids |
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223 | (20) |
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Spatially Adaptive Refinement |
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243 | (20) |
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Asymptotic Expansion Around Principal Components and the Complexity of Dimension Adaptive Algorithms |
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263 | |
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Jochen Garcke is Professor at the Institute of Numerical Simulation, University of Bonn. Michael Griebel is Managing Editor of the journal Numerische Mathematik, series editor of LNCSE and volume editor of the proceedings on Meshfree Methods for PDEs, published as LNCSE 43, 57, 65 and 79.
Lisainfo e-raamatute kohta