The main goal of this paper is to discuss the recent advancements matrix means from positive matrices accretive in a more general setting. In particular, we present form governing well established definition geometric mean, then define arbitrary and functional calculus for matrices. Applications new discussion involve generalizations known inequalities setting that This includes arithmetic-harm...

Ranks and explicit structure of some matrices in the Quantics Tensor Train format, which allows representation with logarithmic complexity in many cases, are investigated. The matrices under consideration are Laplace operator with various boundary conditions in D dimensions and inverse Laplace operator with Dirichlet and Dirichlet-Neumann boundary conditions in one dimension. The minimal-rank e...