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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
29/2010

Generalized Cross Approximation for 3d-tensors

Kishore Kumar Naraparaju and Jan Schneider

Abstract

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 $n$.

Received:
May 28, 2010
Published:
May 28, 2010
MSC Codes:
41A80, 41A63, 15A69
Keywords:
Adaptive Cross Approximation, tensor decomposition, pivot strategy, maximum norm

Related publications

inJournal
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