In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.

We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension. Together...

Given two measured spaces $(X,\mu )$ and $(Y,\nu )$, and a third space $Z$, given two functions $u(x,z)$ and $v(x,z)$, we study the problem of finding two maps $s:X\to Z$ and $t:Y\to Z$ such that the images $s\left(\mu \right)$ and $t\left(\nu \right)$ coincide, and the integral ${\int }_{X}u(x,s\left(x\right))d\mu -{\int }_{Y}v(y,t\left(y\right))d\nu$ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.

Given two measured spaces $(X,\mu )$ and $(Y,\nu )$, and a third space Z, given two functions u(x,z) and v(x,z), we study the problem of finding two maps $s:X\to Z$ and $t:Y\to Z$ such that the images $s\left(\mu \right)$ and $t\left(\nu \right)$ coincide, and the integral ${\int }_{X}u(x,s\left(x\right))d\mu -{\int }_{Y}v(y,t\left(y\right))d\nu$ is maximal. We give condition on u and v for which there is a unique solution.

Mediante integrali multipli agevoli per il calcolo numerico vengono espressi il valore assoluto di un determinante qualsiasi e le formule di Cramer.

We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We also raise...

In this paper, we established a connection between the Laplacian eigenvalues of a signed graph and those of a mixed graph, gave a new upper bound for the largest Laplacian eigenvalue of a signed graph and characterized the extremal graph whose largest Laplacian eigenvalue achieved the upper bound. In addition, an example showed that the upper bound is the best in known upper bounds for some cases.

A method of analysis for a class of descriptor 2D discrete-time linear systems described by the Roesser model with a regular pencil is proposed. The method is based on the transformation of the model to a special form with the use of elementary row and column operations and on the application of a Drazin inverse of matrices to handle the model. The method is illustrated with a numerical example.

We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for $|q_0|=...=|q_{N-1}|=1$ the quantity $\Phi ={\sum }_{i+k=j+l}\frac{q_i{q}_k}{q_j{q}_l}$ satisfies $\Phi \ge N^2$, with equality if and only if $q=\left(q_i\right)$ is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of $\Phi$, (2) the study of the critical points of $\Phi$, and (3) the computation of the moments of $\Phi$. We explore here these questions,...

Compositional data, multivariate observations that hold only relative information, need a special treatment while performing statistical analysis, with respect to the simplex as their sample space ([Aitchison, J.: The Statistical Analysis of Compositional Data. Chapman and Hall, London, 1986.], [Aitchison, J., Greenacre, M.: Biplots of compositional data. Applied Statistics 51 (2002), 375–392.], [Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V. (eds): Compositional data analysis in the geosciences:...