"2014-03-31+02:00"^^ . . . . . "2015-04-23+02:00"^^ . "Krylov subspace methods" . "GA13-06684S" . . " preconditioning" . . . "0"^^ . "Itera\u010Dn\u00ED metody ve v\u00FDpo\u010Detn\u00ED matematice: Anal\u00FDza, p\u0159edpodm\u00EDn\u011Bn\u00ED a aplikace" . . "1"^^ . "2013-02-01+01:00"^^ . . "The project deals with iterative methods for several important problems of numerical linear algebra. It includes their analysis, preconditioning, solving ill-posed problems as well as real-world applications. We focus on Krylov subspace methods, open questions related to their convergence, associated matrix approximation problems, error estimation and stopping criteria. We will study various preconditioning techniques including new algorithms based on incomplete factorizations and orthogonalization schemes, and block saddle-point preconditioning. We intend to analyze regularization methods for solving ill-posed problems in image and signal processing, open problems in total least squares and Golub-Kahan bidiagonalization. An inseparable part of our work are broad international collaboration and selected real-world applications such as the approximation of scattering amplitude and nuclear magnetic resonance."@en . . " total least squares" . "0"^^ . " convergence analysis" . . "Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications"@en . . . "http://www.isvav.cz/projectDetail.do?rowId=GA13-06684S"^^ . . " regularization methods" . . "16"^^ . "Projekt se zab\u00FDv\u00E1 itera\u010Dn\u00EDmi metodami pro \u0159e\u0161en\u00ED n\u011Bkter\u00FDch d\u016Fle\u017Eit\u00FDch probl\u00E9m\u016F numerick\u00E9 line\u00E1rn\u00ED algebry. Projekt zahrnuje anal\u00FDzu konvergence, p\u0159edpodmi\u0148ov\u00E1n\u00ED, \u0159e\u0161en\u00ED nekorektn\u00EDch \u00FAloh, v\u010Detn\u011B jejich re\u00E1ln\u00FDch aplikac\u00ED. Soust\u0159ed\u00EDme se na studium krylovovsk\u00FDch metod, konkr\u00E9tn\u011B na otev\u0159en\u00E9 ot\u00E1zky t\u00FDkaj\u00EDc\u00ED se jejich konvergence a souvisej\u00EDc\u00EDch maticov\u00FDch aproxima\u010Dn\u00EDch probl\u00E9m\u016F, odhady chyb a zastavovac\u00ED krit\u00E9ria. Budou studov\u00E1ny r\u016Fzn\u00E9 p\u0159edpodm\u00ED\u0148ovac\u00ED techniky v\u010Detn\u011B nov\u00FDch algoritm\u016F zalo\u017Een\u00FDch na ne\u00FApln\u00FDch faktorizac\u00EDch a ortogonaliza\u010Dn\u00EDch sch\u00E9matech, jako\u017E i blokov\u00E9 p\u0159edpodm\u00EDn\u011Bn\u00ED pro \u00FAlohy sedlov\u00E9ho bodu. Hodl\u00E1me analyzovat regulariza\u010Dn\u00ED metody pro \u0159e\u0161en\u00ED nekorektn\u00EDch \u00FAloh v oblasti zpracov\u00E1n\u00ED obrazov\u00E9 \u010Di sign\u00E1lov\u00E9 informace. P\u0159edpokl\u00E1d\u00E1me \u0159e\u0161en\u00ED otev\u0159en\u00FDch probl\u00E9m\u016F v \u00FAloh\u00E1ch \u00FApln\u00FDch nejmen\u0161\u00EDch \u010Dtverc\u016F a Golub-Kahanov\u011B bidiagonalizaci. Ned\u00EDlnou sou\u010D\u00E1st\u00ED na\u0161\u00ED pr\u00E1ce je \u0161irok\u00E1 mezin\u00E1rodn\u00ED spolupr\u00E1ce a vybran\u00E9 re\u00E1ln\u00E9 aplikace jako je aproximace amplitudy rozptylu a nukle\u00E1rn\u00ED magnetick\u00E1 rezonance." . . "2017-12-31+01:00"^^ . "16"^^ . "Krylov subspace methods, preconditioning, convergence analysis, regularization methods, total least squares, sparse matrices"@en . .