A popular method for computing the matrix logarithm is the inverse scaling and squaring method, which essentially carries out the steps of the scaling and squaring method for the matrix exponential in reverse order. Here we make several improvements to the method, putting its development on a par with our recent version [SIAM J. Matrix Anal. Appl., 31 (2009), pp. 970–989] of the scaling and squ...

Let F be a field of arbitrary characteristic l, and let q ∈ F ∗. Let e be the least integer such that 1+ q+ · · ·+ q = 0. Let κ be an ecore partition such that it has an e-abacus display in which the number of beads on each runner is nondecreasing as we go from left to right. We study the decomposition numbers dlλμ of q-Schur algebras where μ is a partition having e-core κ and ‘locally small’ e...

Spectral methods are a powerful tool for inferring the parameters of certain classes of probability distributions by means of standard eigenvalueeigenvector decompositions. Spectral algorithms can be orders of magnitude faster than loglikelihood based and related iterative methods, and, thanks to the uniqueness of the spectral decomposition, they enjoy global optimality guarantees. In practice,...

Coupled decompositions of multiple tensors are fundamental tools for multi-set data fusion. In this paper, we introduce a coupled version of the rank-(Lm, Ln, ·) block term decomposition (BTD), applicable to joint independent subspace analysis. We propose two algorithms for its computation based on a coupled block simultaneous generalized Schur decomposition scheme. Numerical results are given ...

This paper presents efficient Schur–type algorithms for estimating the column space (signal subspace) of a low rank data matrix corrupted by additive noise. Its computational structure and complexity are similar to that of an LQ–decomposition, except for the fact that plane and hyperbolic rotations are used. Therefore, they are well suited for a parallel (systolic) implementation. The required ...

Nonsymmetric and highly indefinite linear systems can be quite difficult to solve via iterative methods. This paper combines ideas from the Multilevel Schur Low-Rank preconditioner developed by Y. Xi, R. Li, and Y. Saad [SIAM J. Matrix Anal., 37 (2016), pp. 235–259] with classic block preconditioning strategies in order to handle this case. The method to be described generates a tree structure ...

A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that shar...

Isomorphisms are constructed between generalized Schur algebras in different degrees. The construction covers both the classical case (of general linear groups over infinite fields of arbitrary characteristic) and the quantized case (in type A, for any non-zero value of the quantum parameter q). The construction does not depend on the characteristic of the underlying field or the choice of q 6=...

This paper discusses the Schur complement viewpoint when developing parallel preconditioners for general sparse linear systems. Schur complement methods are pervasive in numerical linear algebra where they represent a canonical way of implementing divide-and-conquer principles. The goal of this note is to give a brief overview of recent progress made in using these techniques for solving genera...