منابع مشابه
Space-Time Approximation with Sparse Grids
In this article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N) degrees of freedom, these spaces involve for d > 1 also only O...
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We present a machine learning approach for the forecasting of time series using the sparse grid combination technique. In this approach, the problem of analyzing a time series is first transformed into a higher-dimensional regression problem based on a delay embedding of the empirical data. Then, a grid-based approach is used to discretize the resulting high-dimensional feature space. In order ...
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In [GOS99], adaptive sparse grid spaces spanned by a finite number of tensor-product L2-orthogonal Haar functions have been applied to capacitance calculations on a unit screen. In this note, we state asymptotically optimal approximation rates for this problem when choosing the best possible adaptive sparse grid space of a given dimension N . We also compare the results with other recent approa...
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The efficient numerical treatment of high-dimensional problems is hampered by the curse of dimensionality. We review approximation techniques which overcome this problem to some extent. Here, we focus on methods stemming from Kolmogorov’s theorem, the ANOVA decomposition and the sparse grid approach and discuss their prerequisites and properties. Moreover, we present energy-norm based sparse gr...
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We present a survey of the fundamentals and the applications of sparse grids, with a focus on the solution of partial differential equations (PDEs). The sparse grid approach, introduced in Zenger (1991), is based on a higherdimensional multiscale basis, which is derived from a one-dimensional multiscale basis by a tensor product construction. Discretizations on sparse grids involve O(N · (logN)...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2006
ISSN: 1064-8275,1095-7197
DOI: 10.1137/050629252