The nearest 'doubly stochastic' matrix to a real matrix with the same first moment

The Nearest Generalized Doubly Stochastic Matrix to a Real Matrix with the same First and Second Moment

Let T be an arbitrary n × n matrix with real entries. We explicitly find the closest (in Frobenius norm) matrix A to T , where A is n × n with real entries, subject to the condition that A is “generalized doubly stochastic” (i.e. Ae = e and eA = e , where e = (1, 1, ..., 1) , although A is not necessarily nonnegative) and A has the same first moment as T (i.e. eT1 Ae1 = e T 1 Te1). We also expl...

Some results on the symmetric doubly stochastic inverse eigenvalue problem

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...

Linear preserving gd-majorization functions from Mn,m to Mn,k

Computing the Nearest Doubly Stochastic Matrix with A Prescribed Entry

In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed (1, 1) entry to a given matrix. According to the well-established dual theory in optimization, the dual of the underlying problem is an unconstrained differentiable but not twice differentiable convex optimization problem. A Newton-type method is ...

Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...