Relative error tensor low rank approximation
We consider relative error low rank approximation of tensors with respect to the Frobenius
norm. Namely, given an order-q tensor A∊ ℝ∏ i= 1 q ni, output a rank-k tensor B for which …
norm. Namely, given an order-q tensor A∊ ℝ∏ i= 1 q ni, output a rank-k tensor B for which …
Multidimensional approximation of nonlinear dynamical systems
A key task in the field of modeling and analyzing nonlinear dynamical systems is the
recovery of unknown governing equations from measurement data only. There is a wide …
recovery of unknown governing equations from measurement data only. There is a wide …
On the minimal algebraic complexity of the rank-one approximation problem for general inner products
K Kozhasov, A Muniz, Y Qi, L Sodomaco - arXiv preprint arXiv:2309.15105, 2023 - arxiv.org
We study the algebraic complexity of Euclidean distance minimization from a generic tensor
to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Veronese …
to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Veronese …
Numerical computation for orthogonal low-rank approximation of tensors
In this paper we study the orthogonal low-rank approximation problem of tensors in the
general setting in the sense that more than one matrix factor is required to be mutually …
general setting in the sense that more than one matrix factor is required to be mutually …
SVD-based algorithms for the best rank-1 approximation of a symmetric tensor
This paper revisits the problem of finding the best rank-1 approximation to a symmetric
tensor and makes three contributions. First, in contrast to the many long and lingering …
tensor and makes three contributions. First, in contrast to the many long and lingering …
Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation
This paper revisits the classical problem of finding the best rank-1 approximation to a
generic tensor. The main focus is on providing a mathematical proof for the convergence of …
generic tensor. The main focus is on providing a mathematical proof for the convergence of …
On orthogonal tensors and best rank-one approximation ratio
As is well known, the smallest possible ratio between the spectral norm and the Frobenius
norm of an m*n matrix with m≤n is 1/m and is (up to scalar scaling) attained only by …
norm of an m*n matrix with m≤n is 1/m and is (up to scalar scaling) attained only by …
A recursive eigenspace computation for the canonical polyadic decomposition
The canonical polyadic decomposition (CPD) is a compact decomposition which expresses
a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is …
a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is …
Guarantees for existence of a best canonical polyadic approximation of a noisy low-rank tensor
E Evert, L De Lathauwer - SIAM Journal on Matrix Analysis and Applications, 2022 - SIAM
The canonical polyadic decomposition (CPD) of a low-rank tensor plays a major role in data
analysis and signal processing by allowing for unique recovery of underlying factors …
analysis and signal processing by allowing for unique recovery of underlying factors …
The tensor-train format and its applications: Modeling and analysis of chemical reaction networks, catalytic processes, fluid flows, and Brownian dynamics
P Gelß - 2017 - refubium.fu-berlin.de
The simulation and analysis of high-dimensional problems is often infeasible due to the
curse of dimensionality. In this thesis, we investigate the potential of tensor decompositions …
curse of dimensionality. In this thesis, we investigate the potential of tensor decompositions …