Tensor density

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Multilinear Low-Rank Tensors on Graphs & Applications

Pierre Vandergheynst, Nauman Shahid, Francesco Grassi

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

2016

Scale-invariant alternatives to general relativity. II. Dilaton properties

Mikhail Chapochnikov, Georgios Karananas

In the present paper, we revisit gravitational theories which are invariant under TDiffs-transverse (volume-preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent diffeomorphism-invar ...

American Physical Society2016

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Siam Publications2016

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Fabio Nobile, Daniel Kressner, Christine Tobler, Rajesh Kumar

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

2015

Mechanism of the Cassie-Wenzel transition via the atomistic and continuum string methods

Simone Meloni

The string method is a general and flexible strategy to compute the most probable transition path for an activated process (rare event). We apply here the atomistic string method in the density field to the Cassie-Wenzel transition, a central problem in th ...

Amer Inst Physics2015

Dynamical Approximation By Hierarchical Tucker And Tensor-Train Tensors

We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434-454], [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2360-2375]) to the re ...

Society for Industrial and Applied Mathematics2013

Light Field Tensor Recovery

Pierre Vandergheynst, Mahdad Hosseini Kamal

This paper presents a novel approach to capture light field in camera arrays based on the tensor recovery framework. Light fields are acquired by a linear array of cameras with overlapping field of view. We represent the light fields in shape of a tensor t ...

2012

Low-rank tensor Krylov subspace methods for parametrized linear systems

Daniel Kressner, Christine Tobler

We consider linear systems A(alpha)x(alpha) - b(alpha) depending on possibly many parameters alpha = (alpha(1), ... , alpha(p)). Solving these systems simultaneously for a standard discretization of the parameter range would require a computational effort ...

Society for Industrial and Applied Mathematics2011

Self-Similar Vector Fields

Pouya Dehghani Tafti

We propose statistically self-similar and rotation-invariant models for vector fields, study some of the more significant properties of these models, and suggest algorithms and methods for reconstructing vector fields from numerical observations, using the ...

EPFL2011

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

Feride Tiglay

We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...

Springer Verlag2010

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