During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

Low rank approximation of matrices has been well studied in literature. Singular value
decomposition, QR decomposition with column pivoting, rank revealing QR factorization …

A simple nonrecursive form of the tensor decomposition in d dimensions is presented. It
does not inherently suffer from the curse of dimensionality, it has asymptotically the same …

Large-scale problems have always been a challenge for numerical computations. An
example is the treatment of fully populated n× n matrices when n2 is close to or beyond the …

In the present paper, we discuss the novel concept of super-compressed tensor-structured
data formats in high-dimensional applications. We describe the multifolding or quantics …

Recently, the format of TT tensors (Hackbusch and Kühn in J Fourier Anal Appl 15: 706–722,
2009; Oseledets in SIAM J Sci Comput 2009, submitted; Oseledets and Tyrtyshnikov in SIAM …

A new method for structured representation of matrices and vectors is presented. The
method is based on the representation of a matrix as ad-dimensional tensor and applying …

In the present paper, we give a survey of the recent results and outline future prospects of
the tensor-structured numerical methods in applications to multidimensional problems in …

We investigate the convergence rate of approximations by finite sums of rank-1 tensors of
solutions of multiparametric elliptic PDEs. Such PDEs arise, for example, in the parametric …

Recently, the method called tensor completion by parallel matrix factorization via tensor train
(TMac-TT) has achieved promising performance on estimating the missing information …