A Multilinear Singular Value Decomposition

In this paper we discuss a multilinear generalization of the best rank-R approximation problem for matrices, namely, the approximation of a given higher-order tensor, in an optimal least-squares sense, by a tensor that has prespecified column rank value,...

Earlier work has shown that no extension of the Eckart--Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart--Young SVD approximation theorem to ...

Let $A$ be a matrix with known singular values and left and/or right singular vectors, and let $A'$ be the matrix obtained by deleting a row from $A$. We present efficient and stable algorithms for computing the singular values and left and/or right ...