Solving Linear Systems Whose Input Data Are Rational Functions of Interval Parameters

Решаване на линейни системи чиито входни данни са рационални функции на интервални параметри Евгения Д. Попова Abstract. sn this p—per we investig—te the —ppli™—tion of — selfEveried gener—lEpurpose parametric xedEpoint iter—tion method to line—r systems involving nonline—r dependen™iesF „he in™lusion method is ™om˜ined with — simple interv—l —rithmeti™ te™hnique providing inner —nd outer ˜ounds for the r—nge of monotone r—tion—l fun™tionsF „he —rithmeti™ on proper —nd improper interv—ls is ™onsidered —s —n intermedi—te ™omput—tion—l tool for elimin—ting the dependen™y pro˜lem in r—nge ™omput—tion —nd for o˜t—ining inner estim—tions ˜y outw—rdly rounded interv—l —rithmeti™F „herefore the t—rget pro˜lems to ˜e solved —re restri™ted to line—r systems whose input d—t— —re r—tion—l fun™tions of un™ert—in p—r—meters v—rying within given interv—lsF ƒupporting softw—re tools with result veri™—tionD developed in the environment of MathematicaD —re presentedF „he dis™ussed methodology —nd softw—re tools ™—n ˜e —pplied to — wide r—nge of pr—™ti™—l pro˜lems le—ding to line—r systems with dependent un™ert—in d—t—D in p—rti™ul—r —ppli™—tions to piw models of me™h—ni™—l stru™turesF feside some illustr—tive ex—mplesD —n —dv—n™ed pr—™ti™—l —ppli™—tion from stru™tur—l engineering me™h—ni™s is solved ˜y the dis™ussed p—r—metri™ iter—tionD —s well —s ˜y — ™om˜in—tion of interv—l te™hniques ˜—sed on the p—r—metri™ solverY the results —re ™omp—red to liter—ture d—t— produ™ed ˜y other methodsF e ™omp—rison of dierent me—sures of overestim—tion is doneF Keywords: line—r systemsD interv—l p—r—metersD nonline—r dependen™iesD —utom—ti™ result veri™—tionD stru™tur—l steel fr—mesF AMS subject classication: ISeHTD TSqPH