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Numerical tensor calculus

delete2014-05-12
delete53
PRE
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Wolfgang Hackbusch *
DOI：10.1017/S0962492914000087delete
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Abstract

Abstract

En 中文
The usual large-scale discretizations are applied to two or three spatial dimensions. The standard methods fail for higher dimensions because the data size increases exponentially with the dimension. In the case of a regular grid with n grid points per direction, a spatial dimension d yields n(d) grid points. A grid function defined on such a grid is an example of a tensor of order d. Here, suitable tensor formats help, since they try to approximate these huge objects by a much smaller number of parameters, which increases only linearly in d. In this way, data of size n(d) = 1000(1000) can also be treated. This paper introduces the algebraic and analytical aspects of tensor spaces. The main part concerns the numerical representation of tensors and the numerical performance of tensor operations.
Keywords:
ELECTRONIC-STRUCTURE CALCULATIONS
KRYLOV SUBSPACE METHODS
LOW-RANK APPROXIMATION
N-TERM APPROXIMATION
HIERARCHICAL TUCKER
LINEAR-SYSTEMS
ORDER TENSOR
DECOMPOSITIONS
COMPUTATIONS
ALGORITHMS
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Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.

Journal

Acta Numerica cover
Acta Numerica
IF:
11.3
Papers:
89
Citations:
3.4K

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No organization information available