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CHEBFUN IN THREE DIMENSIONS
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DOI：10.1137/16M1083803.png)
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Abstract
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We present an algorithm for numerical computations involving trivariate functions in a three-dimensional rectangular parallelepiped in the context of Chebfun. Our scheme is based on low-rank representation through multivariate adaptive cross approximation. The component one-dimensional functions are represented by finite Chebyshev expansions, or trigonometric expansions in the periodic case. Numerical experiments show the power and convenience of Chebfun3 for problems such as function manipulation, differentiation, optimization, and integration, as well as for exploration of fundamental issues of multivariate approximation and low-rank compression.
Keywords:
Chebfun
slice-Tucker decomposition
low-rank approximation
multivariate adaptive cross approximation
MACA
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