Slow Exponential Growth for Gauss Patterson Sparse Grids
نویسنده
چکیده
When Gauss Patterson rules are used to form a sparse grid, the indexing of the underlying 1D family is crucial. It would seem natural to use the indexing that preserves nesting, but this leads to exponential growth in the order of the 1D rules. If the aim is to efficiently construct a family of sparse grids, indexed to achieve a linearly increasing level of precision, then it is possible to preserve the use of nested Gauss Patterson rules while sharply cutting the order growth. This is done by delaying the introduction of the next rule until the precision requirement of the sparse grid demands it.
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