In Markov chain models in finance and healthcare a transition matrix over a certain time interval is needed but only a transition matrix over a longer time interval may be available. The problem arises of determining a stochastic pth root of a stochastic matrix (the given transition matrix). By exploiting the theory of functions of matrices, we develop results on the existence and characterizat...

Abstract Models in which the covariance matrix has structure of a sparse plus low rank perturbation are ubiquitous data science applications. It is often desirable for algorithms to take advantage such structures, avoiding costly computations that require cubic time and quadratic storage. This accomplished by performing operations maintain example, inversion via Sherman–Morrison–Woodbury formul...

We define positive integer roots of finite matrices in the 2×2 case. Where possible, we try to generalise results n×n matrices.

The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W . Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W , skew-Ham...

The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W . Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W , skew-Ham...