This paper deals with the stability of the intersection of a given set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$ X\subset \mathbb{R}^{n}$$</EquationSource> </InlineEquation>with the solution, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$F\subset \mathbb{R}^{n}$$</EquationSource> </InlineEquation>, of a given linear system whose coefficients can be arbitrarily perturbed. In the optimization context, the fixed constraint set X can be the...</equationsource></inlineequation></equationsource></inlineequation>

This paper deals with the stability of the intersection of a given set $$ X\subset \mathbb{R}^{n}$$ with the solution, $$F\subset \mathbb{R}^{n}$$ , of a given linear system whose coefficients can be arbitrarily perturbed. In the optimization context, the fixed constraint set X can be the...

Considers the solution of large systems of linear equations, such as those arising from a large linearized economic model. Recommends (a) that matrix inversion be avoided, in favour of LU methods; and (b) that sparsity in the system be exploited using special computer subroutines. Some examples...

Farkas type results are available for solutions to linear systems. These can also include restrictions such as nonnegative solutions or integer solutions. They show that the unsolvability can be reduced to a single constraint that is not solvable and this condition is implied by the original...

Рассмотрены системы неравенств Ляпунова произвольного порядка. Представлен аналитический способ нахождения решений двойственных систем матричных неравенств....

В статье предложены простейшие линейные локальные алгоритмы непрерывного перемещения агентов для их равномерного расположения на прямой или окружности. При...

This paper concerns the modelling of stochastic processes by means of dynamic factor models. In such models the observed process is decomposed into a structured part called the latent process, and a remainder that is called noise. The observed variables are treated in a symmetric way, so that no...

Global total least squares (GTLS) is a method for the identification of linear systems where no distinction between input and output variables is required. This method has been developed within the deterministic behavioural approach to systems. In this paper we analyse statistical properties of...