We are interested in the following work in the doubly stochastic matrix nearness problem. Instances of this problems occurs in differents fields: aggregation of preferences in operational research, calculus of variations and shape optimisation, etc. We propose here a direct study via the projection theorem and a numerical resolution inspired by the alternating projections algorithm of Boyle-Dyk...

In graph-based clustering, a relevant affinity matrix is crucial for good results. Double stochasticity of the has been shown to be an important condition, both in theory and practice. this paper, we emphasize idempotency as another key condition. fact, theorem from Sinkhorn, R. (1968) allows us exhibit bijective relationship between set doubly stochastic idempotent matrices order n (modulo per...

Our main goal in this paper is to investigate stochastic ternary antiderivatives (STAD). First, we will introduce the random antiderivative operator. Then, by introducing aggregation function using special functions such as Mittag-Leffler (MLF), Wright (WF), H-Fox (HFF), Gauss hypergeometric (GHF), and exponential (EXP-F), select optimal control performing necessary calculations. Next, consider...

Efficient, backward-stable, doubly structure-preserving algorithms for the Hamiltonian symmetric and skew-symmetric eigenvalue problems are developed. Numerical experiments confirm the theoretical properties of the algorithms. Also developed are doubly structure-preserving Lanczos processes for Hamiltonian symmetric and skew-symmetric matrices.

We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where nonsingularity of Jacobian can fail. The optimality conditions this are formulated as system strongly functions. show that does not hold system. By exploiting structure, we construct modified two step Newton guarantees nonsingular at each iteration, and converges to quadratically. Funding: This work ...

Cluster analysis by nonnegative low-rank approximations has experienced a remarkable progress in the past decade. However, the majority of such approximation approaches are still restricted to nonnegative matrix factorization (NMF) and suffer from the following two drawbacks: 1) they are unable to produce balanced partitions for large-scale manifold data which are common in real-world clusterin...

Moderated greedy search is based on the idea that it is helpful for greedy search algorithms to make non-optimal choices “once in a while.” This notion can be made precise by using the majorizationtheoretic approach to greedy algorithms. Majorization is the study of pre-orderings induced by doubly stochastic matrices. A majorization operator when applied to a distribution makes it “less unequal...

A stronger version of the van der Waerden permanent conjecture asserts that if J„ denotes the n X n matrix all of whose entries are \/n and A is any fixed matrix on the boundary of the set ofnxn doubly stochastic matrices, then per(A/4 + (1 — \)Jn) as a function of X is nondecreasing in the interval [0, 1]. In this paper, we elucidate the relation of this assertion to some other conjectures kno...