Generalized cross approximation for 3d-tensors

Generalized cross approximation for 3d-tensors

In this article we present a generalized version of the Cross Approximation for 3d-ten-sors. The given tensor a ∈ R n×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 vec...

Generalized Slow Roll for Tensors

The recent BICEP2 detection of degree scale CMB B-mode polarization, coupled with a deficit of observed power in large angle temperature anisotropy, suggest that the slow-roll parameter H , the fractional variation in the Hubble rate per efold, is both relatively large and may evolve from an even larger value on scales greater than the horizon at recombination. The relatively large tensor contr...

Generalized polarization tensors for shape description

With each domain and material parameter, an infinite number of tensors, called the Generalized Polarization Tensors (GPTs), is associated. The GPTs contain significant information on the shape of the domain. In the recent paper [9], a recursive optimal control scheme to recover fine shape details of a given domain using GPTs is proposed. In this paper, we show that the GPTs can be used for shap...

Fluids Final Project: Generalized Tensors

On best rank one approximation of tensors

Today, compact and reduced data representations using low rank data approximation are common to represent high-dimensional data sets in many application areas as for example genomics, multimedia, quantum chemistry, social networks or visualization. In order to produce such low rank data representations, the input data is typically approximated by so-called alternating least squares (ALS) algori...