Obravnavali smo Schurov razcep, natančneje kako na iterativen način izboljšati obstoječ Schurov razcep v nižji natančnosti do Schurovega razcepa v višji natančnosti. Najprej smo pojasnili, kaj Schurov razcep je, katere probleme rešuje in kakšne so iterativne metode. Predstavili smo algoritem, ki z vsakim korakom izboljša natančnost razcepa, in ga podrobno analizirali. Predelali smo izboljšave in poenostavitve algoritma glede na vrsto vhodne matrike, ter si na praktičnih primerih ogledali delovanje algoritma, predvsem kako večkratno izboljšanje natančnosti še dodatno pohitri pridobivanje razcepa, ko je razlika med začetno in končno natančnostjo dokaj visoka. We introduced the Schur decomposition, its applications and available iterative methods. We have explained what is a Schur decomposition and how can we compute a more accurate decomposition, if we already have an approximate solution. This work is an iterative algorithm for improving the Schur decomposition, which means that it improves the result on each iteration. The analysis and refinement of the algorithm is shown. We have investigated how can we simplify the solution on certain types of matrices and have checked the practical results and accuracy of the algorithm especially the part where we use the algorithm multiple times to improve its accuracy.
