. . "605"^^ . . . . . "605"^^ . "1"^^ . "0"^^ . "Krylov subspace methods; systems of linear equations; stopping criteria; finite precision computation"@en . "3"^^ . . "Metody Krylovov\u00FDch podprostor\u016F-matematick\u00E1 teorie, zastavovac\u00ED krit\u00E9ria a chov\u00E1n\u00ED v aritmetice s kone\u010Dnou p\u0159esnost\u00ED"@cs . "Projekt je zam\u011B\u0159en na jeden z hlavn\u00EDch probl\u00E9m\u016F numerick\u00E9 line\u00E1rn\u00ED algebry - na \u0159e\u0161en\u00ED syst\u00E9m\u016F line\u00E1rn\u00EDch rovnic. Syst\u00E9my rovnic vznikaj\u00ED nap\u0159. p\u0159i modelov\u00E1n\u00ED ve v\u011Bd\u011B a technice a jsou \u010Dasto velmi rozs\u00E1hl\u00E9. K nalezen\u00ED aproximace \u0159e\u0161en\u00ED se pou\u017E\u00EDvaj\u00ED itera\u010Dn\u00ED metody (nap\u0159. krylovovsk\u00E9 metody), je\u017E jsou st\u0159edem na\u0161eho z\u00E1jmu. Pro \u00FAsp\u011B\u0161nou aplikaci t\u011Bchto metod v praxi je nutn\u00E9 (mimo jin\u00E9) pochopit principy na kter\u00FDch funguj\u00ED (popsat konvergenci v z\u00E1vislosti na vstupn\u00EDch datech) a chov\u00E1n\u00ED v kone\u010Dn\u00E9 aritmetice po\u010D\u00EDta\u010De. Velmi d\u016Fle\u017Eitou a praktickou ot\u00E1zkou je tak\u00E9 zastavovac\u00ED krit\u00E9rium v\u00FDpo\u010Dtu (zji\u0161\u0165ov\u00E1n\u00ED kvality vypo\u010Dten\u00E9 aproximace \u0159e\u0161en\u00ED). Budeme zkoumat v\u00FD\u0161e uveden\u00E9 probl\u00E9my. Povaha projektu vy\u017Eaduje pou\u017Eit\u00ED matematick\u00FDch n\u00E1stroj\u016F z mnoha oblast\u00ED nap\u0159. funkcion\u00E1ln\u00ED anal\u00FDzy, teorie perturbac\u00ED, numerick\u00E9 anal\u00FDzy, teorie matic a numerick\u00E9 line\u00E1rn\u00ED algebry."@cs . "3"^^ . . . "The project deals with solving systems of linear equations (one of the basic problems of numerical linear algebra). Such systems arise e.g. from mathematical modeling of problems in sciences and engineering and they are often very large. In order to find an approximation of the solution we use interative methods (e.g. Krylov subspace methods). To apply these methods in practice, we need to understand (among the others) principles they are based on (convergence in dependence on input data) and behaviour in finite precision arithmetic. Very important and practical questions are how to evaluate the accuracy of the computed approximate solution and when to stop the computation, We will tnvestigate these questions. The nature of this project will require use of mathematical tools from many different areas e.g. functional analysis, perturbation theory, numerical analysis, matrix theory and numerical linear algebra."@en . "0"^^ . "Krylov subspace methods-mathematical theory, stopping criteria and behaviour in finite precision arithmetic"@en .