منابع مشابه
Adaptive sparse grids
Sparse grids, as studied by Zenger and Griebel in the last 10 years have been very successful in the solution of partial differential equations, integral equations and classification problems. Adaptive sparse grid functions are elements of a function space lattice. It is seen that such lattices allow the generalisation of sparse grid techniques to the fitting of very high-dimensional functions ...
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Sparse grids have become an important tool to reduce the number of degrees of freedom of discretizations of moderately high-dimensional partial differential equations; however, the reduction in degrees of freedom comes at the cost of an almost dense and unconventionally structured system of linear equations. To guarantee overall efficiency of the sparse grid approach, special linear solvers are...
متن کاملAdaptive Sparse Grids for Hyperbolic Conservation Laws
We report on numerical experiments using adaptive sparse grid dis-cretization techniques for the numerical solution of scalar hyperbolic conservation laws. Sparse grids are an eecient approximation method for functions. Compared to regular, uniform grids of a mesh parameter h contain h ?d points in d dimensions, sparse grids require only h ?1 jloghj d?1 points due to a truncated , tensor-produc...
متن کاملSparse grids
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)...
متن کاملDensity Estimation with Adaptive Sparse Grids for Large Data Sets
Nonparametric density estimation is a fundamental problem of statistics and data mining. Even though kernel density estimation is the most widely used method, its performance highly depends on the choice of the kernel bandwidth, and it can become computationally expensive for large data sets. We present an adaptive sparse-grid-based density estimation method which discretizes the estimated dens...
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ژورنال
عنوان ژورنال: ANZIAM Journal
سال: 2003
ISSN: 1445-8810
DOI: 10.21914/anziamj.v44i0.685