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MiS Preprint

Generalized Cross Approximation for 3d-tensors

Kishore Kumar Naraparaju and Jan Schneider


In this article we present a generalized version of the Cross Approximation for 3d- tensors. The given tensor $a\in\mathbb{R}^{n\times n\times n}$ 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 $n$.

MSC Codes:
41A80, 41A63, 15A69
Adaptive Cross Approximation, tensor decomposition, pivot strategy, maximum norm

Related publications

2011 Repository Open Access
Kishore Kumar Naraparaju and Jan Schneider

Generalized cross approximation for 3d-tensors

In: Computing and visualization in science, 14 (2011) 3, pp. 105-115