Generalized Cross Approximation for 3d-tensors
Kishore Kumar Naraparaju and Jan Schneider
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Submission date: 28. May. 2010
published in: Computing and visualization in science, 14 (2011) 3, p. 105-115
DOI number (of the published article): 10.1007/s00791-011-0166-4
MSC-Numbers: 41A80, 41A63, 15A69
Keywords and phrases: Adaptive Cross Approximation, tensor decomposition, pivot strategy, maximum norm
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In this article we present a generalized version of the Cross Approximation for 3d- tensors. The given tensor a ∈ ℝn×n×n is represented as a matrix of vectors and 2d adaptive Cross Approximation is applied in a nested way to get the tensor decomposition. The main focus lies on theoretical issues of the construction such as the desired interpolation property or the explicit formulas for the vectors in the decomposition. The computational complexity of the proposed algorithm is shown to be linear in n.