Functional Tucker Approximation Using Chebyshev Interpolation

نویسندگان

چکیده

This work is concerned with approximating a trivariate function defined on tensor-product domain via evaluations. Combining tensorized Chebyshev interpolation Tucker decomposition of low multilinear rank yields approximations that can be computed and stored very efficiently. The existing Chebfun3 algorithm [Hashemi Trefethen, SIAM J. Sci. Comput., 39 (2017)]uses similar format but the construction approximation proceeds indirectly, so called slice-Tucker decomposition. As consequence, sometimes uses unnecessarily many evaluations does not fully benefit from potential to reduce, dramatically, computational cost. We propose novel Chebfun3F utilizes univariate fibers instead bivariate slices construct reduces cost for in terms number nearly all functions considered, typically by 75%, over 98%.

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ژورنال

عنوان ژورنال: SIAM Journal on Scientific Computing

سال: 2021

ISSN: ['1095-7197', '1064-8275']

DOI: https://doi.org/10.1137/20m1356944