Any nonsingular matrix has pth roots. One way to compute matrix pth roots is via a specialized version of Newton’s method, but this iteration has poor convergence and stability properties in general. A Schur algorithm for computing a matrix pth root that generalizes methods of Björck and Hammarling [Linear Algebra Appl., 52/53 (1983), pp. 127–140] and Higham [Linear Algebra Appl., 88/89 (1987),...

The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics QCD , and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the t...

We approximate polynomial roots numerically as the eigenvalues of a unitary diagonal plus rank-one matrix. We rely on our earlier adaptation of the algorithm, which exploits the semiseparable matrix structure to approximate the eigenvalues in a fast and robust way, but we substantially improve the performance of the resulting algorithm at the initial stage, as confirmed by our numerical tests.

Let A = (aij) be a real n n matrix with non-negative entries which are weakly increasing down columns. If B = (bij) is the n n matrix where bij := aij+z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several special cases of the conjecture.

Let A = (a ij) be a real n n matrix with non-negative entries which are weakly increasing down columns. If B = (b ij) is the nn matrix where b ij := a ij +z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several special cases of the conjecture.

Recently we proposed to extend the matrix sign classical iteration to the approximation of the real eigenvalues of a companion matrix of a polynomial and consequently to the approximation of its real roots. In our present paper we advance this approach further by combining it with the alternative square root iteration for polynomials and also show a variation using repeated squaring in polynomi...

We show that finding roots of Boolean matrices is an NPhard problem. This answers a twenty year old question from semigroup theory. Interpreting Boolean matrices as directed graphs, we further reveal a connection between Boolean matrix roots and graph isomorphism, which leads to a proof that for a certain subclass of Boolean matrices related to subdivision digraphs, root finding is of the same ...

Let S be a random nonnegative definite matrix and let G be an orthogonal matrix such that S = GDG', where D is the diagonal matrix of the latent roots of S. In this note, we prove _ r G t t Gt21 the a.s. existence of G~I, where G-tc2~ c=j, under some weak conditions on the distribution of S. AMS Subject Classification: Primary 62H10, 60D05.

We introduce improved model for sparseness constrained nonnegative matrix factorization (sNMF) of amplitude mixtures nuclear magnetic resonance (NMR) spectra into greater number of component spectra. In proposed method selected sNMF algorithm is applied to the square of the amplitude of the mixtures NMR spectra instead to the amplitude spectra itself. Afterwards, the square roots of separated s...