# Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4

Valentić, Grgur (2016) Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

In this work we have presented the Jacobi method for Hermitian matrices of order 4 defined by a general cyclic pivot strategy. We have introduced equivalence relations $\sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p}$on the set of cyclic strategies and shown that convergence of the method under some strategy implies convergence of the method under an equivalent strategy. Then we have shown the global convergence of the method under the strategies from the special family $C_1$ and under one parallel strategy. Using a computer program, we have partitioned the set of 720 cyclic strategies in 5 equivalence classes. For each class we have found a strategy for which the method is convergent. That is enough to show the global convergence of the method under all 720 cyclic strategies.