In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
The paper surveys some recent results on iterative aggregation/disaggregation methods (IAD) for computing stationary probability vectors of stochastic matrices and solutions of Leontev linear systems. A particular attention is paid to fast IAD methods.
This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the algebraic structure in which classical addition and multiplication are replaced by and , where . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 and T5 solvability and give necessary and...
Mediante integrali multipli agevoli per il calcolo numerico vengono espressi il valore assoluto di un determinante qualsiasi e le formule di Cramer.
In this paper, we consider the problem of solving a linear algebraic equation in a distributed way by a multi-agent system with a solvability verification requirement. In the problem formulation, each agent knows a few columns of , different from the previous results with assuming that each agent knows a few rows of and . Then, a distributed continuous-time algorithm is proposed for solving the linear algebraic equation from a distributed constrained optimization viewpoint. The algorithm is...
The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As particular results, we provide different properties of the group inverse and we characterize EP endomorphisms of arbitrary vector spaces from the coincidence of the group inverse and the Moore-Penrose inverse.