In this paper, linear stabilities of the top lid driven cavity flows are analyzed, where equations governing disturbances of azimuthal wavenumbers are solved numerically. By operating linear stability analyses, disturbances of wave number one are observed over critical Reynolds number Re_c=2117.

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The problem to find a congruent transformation to make more than one given matrices as diagonal as possible is called the non-orthogonal joint diagonalization problem. While various iterative algorithms have been proposed for the problem, they take long time for large scale problems. It is therefore important to accelerate these algorithms. In this study, we propose a hybrid algorithm that combines two conventional algorithms to reduce the iteration number. Numerical experiments show that the iteration number of the proposed algorithm is 50% smaller than that of the conventional one in the best case.

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