Kronecker regression is a highly-structured least squares problem $\min_ {\mathbf
{x}}\lVert\mathbf {K}\mathbf {x}-\mathbf {b}\rVert_ {2}^ 2$, where the design matrix $\mathbf …

The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in
molecular simulations, high-order correlation functions, and optimization. In this paper, we …

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high
dimensional function approximations arising from computational and data sciences. Various …

This work studies the combinatorial optimization problem of finding an optimal core tensor
shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an …

We implement an efficient data compression algorithm that reduces the memory footprint of
spatial datasets generated during scientific simulations. Storing regularly these datasets is …

A novel framework for hierarchical low‐rank matrices is proposed that combines an adaptive
hierarchical partitioning of the matrix with low‐rank approximation. One typical application is …

We propose a novel rank-adaptive higher-order orthogonal iteration (HOOI) algorithm to
compute the truncated Tucker decomposition of higher-order tensors with a given error …

In this paper, we propose a novel rank-adaptive higher-order orthogonal iteration (RA-HOOI)
algorithm to solve the fixed-accuracy low multilinear-rank approximation of tensors. On the …

Tensor numerical methods, based on the rank-structured tensor representation of d-variate
functions and operators discretized on large n⊗ d grids, are designed to provide O (dn) …

We present ATC, a C++ library for advanced Tucker-based lossy compression of dense
multidimensional numerical data in a shared-memory parallel setting, based on the …