‎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 ...

We present a novel method for approximately equilibrating a matrix using only multiplication by the matrix and its transpose. Our method is based on convex optimization and projected stochastic gradient descent, using an unbiased estimate of a gradient obtained by a randomized method. Our method provably converges in expectation and empirically gets good results with a small number of iteration...

The problem of solving sparse Systems of Linear Algebraic Equations (SLAE) by parallel Monte Carlo numerical methods is considered. The almost optimal Monte Carlo algorithms are presented. In case when a copy of the non-zero matrix elements is sent to each processor the execution time for solving SLAE by Monte Carlo on p processors is bounded by O(nNdT/p) where N is the number of chains, T is t...

in this paper we study the concept of latin-majorizati-on. geometrically this concept is different from other kinds of majorization in some aspects. since the set of all $x$s latin-majorized by a fixed $y$ is not convex, but, consists of :union: of finitely many convex sets. next, we hint to linear preservers of latin-majorization on $ mathbb{r}^{n}$ and ${m_{n,m}}$.

A new method for feature extraction and recognition, namely the fuzzy bidirectional weighted sum criterion (FBWSC) is proposed in this paper. FBWSC defines the row directional fuzzy image optimal image projection matrix. Subsequently, each sample in the original training sample set is transformed using the row directional optimal image projection matrix, and the row directional feature training...

8 Elementary operations and the rank of a matrix 25 8.1 Gauss transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 8.2 Elementary row operations . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.3 The augmented matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.4 Row reducing a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 8.5 Elem...

The central problem of concern to Serrano, Boguña and Vespignani [1] can be effectively and elegantly addressed using a well-established two-stage algorithm that has been applied to internal migration flows for numerous nations and several other forms of ”transaction flow data” [2, 3, 4]. In the first stage, the N row and N column sums of the N × N matrix of weighted, directed network flows (fi...

A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When points reside Euclidean space, a widespread approach to form by Gaussian kernel with pairwise distances, and follow certain normalization (e.g., row-stochastic or its symmetric variant). We demonstrate that doubly stochastic zero main diagonal (i.e., no...

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

Latent block models are used for probabilistic biclustering, which is shown to be an effective method analyzing various relational data sets. However, there has been no statistical test determining the row and column cluster numbers of latent models. Recent studies have constructed statistical-test-based methods stochastic models, assume that observed matrix a square symmetric assignments same ...