Tensor rank bounds and explicit QTT representations for the inverses of circulant matrices

Bounds for Inverses of Triangular Toeplitz Matrices

This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent...

The explicit representations of the Drazin inverses of a class of block matrices

Ela the Explicit Representations of the Drazin Inverses of a Class of Block Matrices

Let M = A B C D be a 2 × 2 block matrix, where ABC = 0 and either DC = 0 or BD = 0. This paper gives the explicit representations of M D in terms of A, B, C, D, A D , (BC) D and D D .

Tensor-Train Ranks for Matrices and Their Inverses

We show that the recent tensor-train (TT) decompositions of matrices come up from its recursive Kronecker-product representations with a systematic use of common bases. The names TTM and QTT used in this case stress the relation with multilevel matrices or quantization that increases artificially the number of levels. Then we investigate how the tensor-train ranks of a matrix can be related to ...

QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images

Quantics tensor train (QTT), a new data-sparse format for one– and multi–dimensional vectors, is based on a bit representation of mode indices followed by a separation of variables. A radix-2 reccurence, that lays behind the famous FFT algorithm, can be efficiently applied to vectors in the QTT format. If input and all intermediate vectors of the FFT algorithm have moderate QTT ranks, the resul...