. "residual arithmetic modular arithmetic systems of linear equations"@en . . . "http://www.isvav.cz/projectDetail.do?rowId=GAP103/12/2377"^^ . "1"^^ . "Study of properties of residual arithmetic for solving sets of linear equations"@en . . . "2015-04-23+02:00"^^ . "Odlo\u017Een\u00E1 z\u00E1v\u011Bre\u010Dn\u00E1 zpr\u00E1va"@cs . "0"^^ . . . . "7"^^ . . . . "7"^^ . "2016-12-31+01:00"^^ . . . . "Na\u0161\u00EDm c\u00EDlem je studium vlastnost\u00ED v\u00EDcemodulov\u00E9 residu\u00E1ln\u00ED aritmetiky p\u0159i \u0159e\u0161en\u00ED specifick\u00FDch probl\u00E9m\u016F line\u00E1rn\u00ED algebry. Jedn\u00EDm z komplexn\u00EDch a vhodn\u00FDch probl\u00E9m\u016F je \u0159e\u0161en\u00ED velk\u00FDch soustav line\u00E1rn\u00EDch rovnic. Toto vy\u017Eaduje vytvo\u0159it model \u0159e\u0161i\u010De za \u00FA\u010Delem prov\u00E1d\u011Bn\u00ED experiment\u016F. Jako z\u00E1klad \u0159e\u0161i\u010De je zvolena metoda Gauss-Jordanovy eliminace s residu\u00E1ln\u00ED pivotizac\u00ED. Za \u00FA\u010Delem z\u00EDsk\u00E1n\u00ED co nejv\u011Brohodn\u011Bj\u0161\u00EDch poznatk\u016F o vlastnostech pou\u017Eit\u00E9 aritmetiky v dan\u00E9m modelu bude pro n\u011Bj vytvo\u0159ena hardwarov\u00E1 architektura, kter\u00E1 bude n\u00E1sledn\u011B emulov\u00E1na pomoc\u00ED FPGA. Experiment\u00E1ln\u00ED \u0159e\u0161en\u00ED n\u00E1m umo\u017En\u00ED tak\u00E9 verifikovat teoretick\u00E9 p\u0159edpoklady o prostorov\u00E9, \u010Dasov\u00E9 a komunika\u010Dn\u00ED slo\u017Eitosti modelovan\u00E9ho \u0159e\u0161i\u010De." . "Deferred Final Report"@en . "GAP103/12/2377" . . . "Studium vlastnost\u00ED residu\u00E1ln\u00ED aritmetiky pro \u0159e\u0161en\u00ED soustav line\u00E1rn\u00EDch rovnic" . "Our intention is to study the properties of the multiple-modulus residual arithmetic with respect to specific numerical problems of linear algebra. One of complex problems of linear algebra suitable for our purpose is solving large systems of linear equations. This requires to create a model of a solver for performing experiments. The method of Gauss-Jordan elimination with residual pivoting is chosen as the base of the solver. In order to gain precise knowledge about the arithmetic used in the model, a hardware architecture of the model will be emulated on FPGA. This experimantal solution enables us also verify the theoretical predicition about the spatial, temporal and communication complexity of the modeled solver."@en . "0"^^ . "2014-04-18+02:00"^^ . . "2012-01-01+01:00"^^ .