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Sparse Grid-Based Nonlinear Filtering
IEEE Transactions on Aerospace and Electronic Systems, 2013The problem of estimating the state of a nonlinear stochastic plant is considered. Unlike classical approaches such as the extended Kalman filter, which are based on the linearization of the plant and the measurement model, we concentrate on the nonlinear filter equations such as the Zakai equation.
Carolyn Kalender, Alfred Schottl
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Sparse Grids, Adaptivity, and Symmetry
Computing, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Scientific Visualization on Sparse Grids
Scientific Visualization Conference (dagstuhl '97), 1997The ever growing size of data sets resulting from industrial and scientific simulations and measurements have created an enormous need for analysis tools allowing interactive visualization. A promising hierarchical approach in the area of numerical simulation is called sparse grids.
C. Teitzel, M. Hopf, T. Ertl
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Numerical integration using sparse grids
Numerical Algorithms, 1998The authors consider various constructions for multivariate quadrature formulas on sparse grids based on Newton-Cotes, Clenshaw-Curtis, Gauss and extended Gauss formulas. They present known results concerning the computational cost and error bounds and indicate a numerically stable implementation. A generalization of \textit{S. A.
Gerstner, Thomas, Griebel, Michael
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Visualizing sparse gridded data sets
IEEE Computer Graphics and Applications, 2000Gridded data sets with many missing values pose a problem because most visualization algorithms fail when presented with incomplete cells. We discuss visualization methods that handle this problem. Our primary interest is developing 3D images for Next-Generation Radar (Nexrad), a weather radar that makes a series of conical scans.
S. Djurcilov, A. Pang
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Volume visualization on sparse grids
Computing and Visualization in Science, 1999Volume rendering is an important technique of displaying volumetric three-dimensional scalar data sets resulting from measurement or simulation. Additionally, sparse grids are of increasing interest in numerical simulations. Based upon hierarchical tensor product bases, the sparse grid approach is a very efficient one improving the ratio of invested ...
Christian Teitzel +3 more
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Spline interpolation on sparse grids
Applicable Analysis, 2011We investigate the rate of convergence of interpolating splines with respect to sparse grids for Besov spaces of dominating mixed smoothness (tensor product Besov spaces). Main emphasis is given to the approximation by piecewise linear functions.
Winfried Sickel, Tino Ullrich
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Sampling inequalities for sparse grids
Numerische Mathematik, 2016The authors use a construction technique (Smolyak algorithm) to build a multivariate operator on a sparse grid having almost the same convergence properties as the univariate operator from which it was constructed. Polynomial reproductions are used. Then some sampling inequalities for functions from mixed regularity Sobolev spaces on sparse grids are ...
Rieger, Christian, Wendland, Holger
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2010
This chapter is concerned with sparse grid (SG) quadrature methods. These methods are constructed using certain combinations of tensor products of one-dimensional quadrature rules. They can exploit the smoothness of f, overcome the curse of dimension to a certain extent and profit from low effective dimensions, see, e.g., [16, 44, 45, 57, 116, 146].
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This chapter is concerned with sparse grid (SG) quadrature methods. These methods are constructed using certain combinations of tensor products of one-dimensional quadrature rules. They can exploit the smoothness of f, overcome the curse of dimension to a certain extent and profit from low effective dimensions, see, e.g., [16, 44, 45, 57, 116, 146].
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Nonlinear Filtering Using Sparse Grids
2011This paper presents a new nonlinear filtering algorithm applicable in realtime. Nonlinear filtering problems are mostly solved with the Extended Kalman Filter which due to the nonlinearities is a suboptimal estimator. Optimal estimates are provided by Fokker-Planck-Equation in combination with Bayes rule.
Carolyn Kalender, Alfred Schöttl
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