to the interval linear tolerance, and control
Sergey P. SrtsRM · 1996
In this paper, the ident(fitzahm probl~n, the tolermu:e probl~n, and the amtrol problon are treated for the interval linear equation Az = b. These problems require computing ;in inner approximatiem of the unitM .~h,ion. sa Es~(A, b) = {x E R n I (3A ~ A)(Ax ~ b)},-f the tolerable sohaion .~et ~vS(A, b) = {x R '~ ] (VA E A)(Ax ~ b)}, and of the cmmoltabte.~dtaion.*a E~v(A,b) = {X e R n ] (Vb ~ b)(Ax B b)} respectively. An dgebredc appn~u:h to their ~flution is developed in which the initial problem is replaced by that of finding an ,dgebrtdc mhalon of some attxiliary interval linear system in Kaucher extended interwfl arithmetic. The algebraic approach is proved almost always m give indusion-maximal inner interval estinmtes of the .~,luti~m sets c, nsidered. We investigate basic prnperties of the algebraic .~*lutions to the interval linear systems and prop.se a nmnber of numerical methods to compute them. In particular, we present the Simple and last suMifferetaial Nnotmt method, prove its convergence and discuss numerical experiments.