مرکز منطقه ای اطلاع رساني علوم و فناوري - Robust solutions of perturbed linear equations

DocumentCode :

823219

Title :

Robust solutions of perturbed linear equations

Author :

Barmish, B. Ross

Author_Institution :

Yale University, New Haven, CT, USA

Volume :

Issue :

fYear :

1977

fDate :

2/1/1977 12:00:00 AM

Firstpage :

123

Lastpage :

124

Abstract :

A perturbed system of linear equalities $\\langle a_{i},x \\rangle = b_{i}, i = 1,2,...,n;a_{i} \\inA_{i};b_{i},\\inB_{i};x\\inX$ (the sets Aiand the intervals Biprescribed a priori) is said to be robust if a solution vector $x_{0}\\in X$ can be found resulting in $\\langle a_{i},x_{0}\\rangle \\in B_{i}$ for all $a_{i} \\in A_{i}$ and all $i = 1, 2,...,n$ . A numerical "test for robustness" is developed. This test is seen to involve 2n parameters at most-even when the solution set $X$ is an infinite-dimensional vector space.