. "16377616"^^ . . "Numerick\u00E9 \u0159e\u0161en\u00ED soustav line\u00E1rn\u00EDch rovnic"@cs . "12367"^^ . "1305"^^ . . . "\u0158e\u0161en\u00ED velk\u00FDch syst\u00E9m\u016F line\u00E1rn\u00EDch algebraick\u00FDch rovnic je jednou z nejd\u016Fle\u017Eit\u011Bj\u0161\u00EDch \u00FAloh numerick\u00E9 matematiky. Pou\u017E\u00EDvaj\u00ED se zejm\u00E9na r\u016Fzn\u00E9 metody na b\u00E1zi klasick\u00E9 Gaussovy elimina\u010Dn\u00ED metody (GEM), jako GEM s pivotac\u00ED, Cholesk\u00E9ho, LU, LUP a QR rozklad, nebo tzv. multigridn\u00ED metody. Velice d\u016Fle\u017Eit\u00E1 je t\u0159\u00EDda probl\u00E9m\u016F s velik\u00FDmi maticemi soustav, ve kter\u00FDch p\u0159ipad\u00E1 jen m\u00E1lo nenulov\u00FDch koeficient\u016F na jeden \u0159\u00E1dek matice (takovou matici naz\u00FDv\u00E1me \u0159\u00EDdk\u00E1). Pro tyto soustavy maj\u00ED nejv\u011Bt\u0161\u00ED v\u00FDznam tzv."@cs . . . "Numerick\u00E9 \u0159e\u0161en\u00ED soustav line\u00E1rn\u00EDch rovnic"@cs . . . . . . . "\u0158e\u0161en\u00ED velk\u00FDch syst\u00E9m\u016F line\u00E1rn\u00EDch algebraick\u00FDch rovnic je jednou z nejd\u016Fle\u017Eit\u011Bj\u0161\u00EDch \u00FAloh numerick\u00E9 matematiky. Pou\u017E\u00EDvaj\u00ED se zejm\u00E9na r\u016Fzn\u00E9 metody na b\u00E1zi klasick\u00E9 Gaussovy elimina\u010Dn\u00ED metody (GEM), jako GEM s pivotac\u00ED, Cholesk\u00E9ho, LU, LUP a QR rozklad, nebo tzv. multigridn\u00ED metody. Velice d\u016Fle\u017Eit\u00E1 je t\u0159\u00EDda probl\u00E9m\u016F s velik\u00FDmi maticemi soustav, ve kter\u00FDch p\u0159ipad\u00E1 jen m\u00E1lo nenulov\u00FDch koeficient\u016F na jeden \u0159\u00E1dek matice (takovou matici naz\u00FDv\u00E1me \u0159\u00EDdk\u00E1). Pro tyto soustavy maj\u00ED nejv\u011Bt\u0161\u00ED v\u00FDznam tzv. itera\u010Dn\u00ED metody, kter\u00E9 n\u00E1m umo\u017E\u0148uj\u00ED na rozd\u00EDl od soustav zalo\u017Een\u00FDch na GEM vyu\u017E\u00EDt pln\u011B \u0159\u00EDdkost matice. Tyto metody hledaj\u00ED \u0159e\u0161en\u00ED soustavy jen p\u0159ibli\u017En\u011B, pomoc\u00ED posloupnosti iterac\u00ED. Zn\u00E1m\u00FDmi u\u010Debnicov\u00FDmi p\u0159\u00EDklady jsou klasick\u00E1 Jacobiho metoda a Gauss-Seidelova metoda. St\u00E1le je\u0161t\u011B maj\u00ED v\u00FDznam relaxa\u010Dn\u00ED metody. Nejpou\u017E\u00EDvan\u011Bj\u0161\u00ED jsou v\u0161ak v sou\u010Dasnosti projektivn\u00ED metody.V\u00FDznamnou podt\u0159\u00EDdou \u0159\u00EDdk\u00FDch soustav, kdy se zpravidla op\u011Bt vrac\u00EDme k prvn\u00ED t\u0159\u00EDd\u011B metod, jsou takzvan\u00E9 soustavy s p\u00E1sovou matic\u00ED.en:Numerical analysis#Solving equations and systems of equations"@cs . . . "12"^^ . . . .