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.
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