A Fast Algorithm for Orthogonal Polynomial Expansions on Sparse Grids∗
نویسندگان
چکیده
A fast algorithm is developed to compute orthogonal polynomial expansions on sparse grids for a function of d variables in a weighted L space. The proposed algorithm combines the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space and a fast algorithm of computing hierarchically structured basis functions. The overall computational complexity of the algorithm is O(n log n) where n is the highest polynomial degree in one dimension. Exponential convergence under an analyticity assumption is proved. Numerical experiments confirm the theoretical results and demonstrate the efficiency of the proposed algorithm.
منابع مشابه
Orthogonal polynomial expansions on sparse grids
We study the orthogonal polynomial expansion on sparse grids for a function of d variables in a weighted L space. A fast algorithm is developed to compute the orthogonal polynomial expansion by combining the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space, and a fast algorithm of computing hierarc...
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