Sparse Grids and Applications

Chapter 1 An Adaptive Sparse Grid Approach for Time Series Prediction

Chapter 2 Efficient Analysis of High Dimensional Data in Tensor Formats

Chapter 3 Sparse Grids in a Nutshell

Chapter 5 Dimension- and Time-Adaptive Multilevel Monte Carlo Methods

Chapter 6 An Efficient Sparse Grid Galerkin Approach for the Numerical Valuation of Basket Options Under Kou’s Jump-Diffusion Model

Chapter 7 The Use of Sparse Grid Approximation for the r -Term Tensor Representation

Chapter 8 On Multilevel Quadrature for Elliptic Stochastic Partial Differential Equations

Chapter 9 Local and Dimension Adaptive Stochastic Collocation for Uncertainty Quantification

Chapter 10 The Combination Technique for the Initial Value Problem in Linear Gyrokinetics

Chapter 11 Model Reduction with the Reduced Basis Method and Sparse Grids

Chapter 12 Spatially Adaptive Refinement

Chapter 13 Asymptotic Expansion Around Principal Components and the Complexity of Dimension Adaptive Algorithms