the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton's method, but previous researchers have mentioned that some...

The computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. It is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of New-ton's method, but previous researchers have mentioned that some iter...

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...

Newton’s method for the inverse matrix pth root, A−1/p, has the attraction that it involves only matrix multiplication. We show that if the starting matrix is cI for c ∈ R then the iteration converges quadratically to A−1/p if the eigenvalues of A lie in a wedge-shaped convex set containing the disc { z : |z−cp| < cp }. We derive an optimal choice of c for the case where A has real, positive ei...

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),...

If A is a matrix with no negative real eigenvalues and all zero eigenvalues of A are semisimple, the principal pth root of A can be computed by Newton’s method or Halley’s method, with a preprocessing procedure if necessary. We prove a new convergence result for Newton’s method, and discover an interesting property of Newton’s method and Halley’s method in terms of series expansions. We explain...

Cardinal’s matrix version of the Sebastiao e Silva polynomial root-finder rapidly approximates the roots as the eigenvalues of the associated Frobenius matrix. We preserve rapid convergence to the roots but amend the algorithm to allow input polynomials with multiple roots and root clusters. As in Cardinal’s algorithm, we repeatedly square the Frobenius matrix in nearly linear arithmetic time p...

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

In applications as in future MIMO communication systems a massive computation of complex matrix operations, such as QR decomposition, is performed. In these matrix operations, the functions roots, inverse and inverse roots are computed in large quantities. Therefore, to obtain high enough performance in such applications, efficient algorithms are highly important. Since these algorithms need to...