Quantum mechanics

Algorithm

Gaussian

Scheme (mathematics)

Low-rank approximation

Pure mathematics

Division algebra

Random projection

Applied mathematics

Rank (graph theory)

Computation

Eigenvalues and eigenvectors

Power (physics)

Mathematical optimization

Projection (relational algebra)

Tensor (intrinsic definition)

Multilinear map

Physics

Singular value decomposition

Mathematics

Multilinear algebra

Mathematical analysis

Combinatorics

Filtered algebra

Singular value

Algebra over a field

SIAM Journal on Matrix Analysis and Applications

This paper is devoted to the computation of low multilinear rank approximations of tensors. Combining the stretegy of power scheme, random projection, and singular value decomposition, we derive a three-stage randomized algorithm for the low multilinear rank approximation. Based on the singular values of sub-Gaussian matrices, we derive the error bound of the proposed algorithm with high probability. We illustrate the proposed algorithms via several numerical examples.

The Computation of Low Multilinear Rank Approximations of Tensors via Power Scheme and Random Projection