Sparse Grid
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High Quality Content by WIKIPEDIA articles! Sparse grids are a numerical technique to represent, integrate or interpolate high dimensional functions. They were originally found by the Russian mathematician Smolyak and are based on a sparse tensor product construction. Computer algorithms for efficient implementations of such grids were later developed by Michael Griebel and Christoph Zenger. The standard way of representing multidimensional functions are tensor or full grids. The number of basis functions or nodes (grid points) that have to be stored and processed depend exponentially on the n...
High Quality Content by WIKIPEDIA articles! Sparse grids are a numerical technique to represent, integrate or interpolate high dimensional functions. They were originally found by the Russian mathematician Smolyak and are based on a sparse tensor product construction. Computer algorithms for efficient implementations of such grids were later developed by Michael Griebel and Christoph Zenger. The standard way of representing multidimensional functions are tensor or full grids. The number of basis functions or nodes (grid points) that have to be stored and processed depend exponentially on the number of dimensions. Even with today's computational power it is not possible to process functions with more than 4 or 5 dimensions. The curse of dimension is expressed in the order of the integration error that is made by a quadrature of level l, with Nl points. The function has regularity r, i.e. is r times differentiable. The number of dimensions is d.
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