Asymptotic quadratic convergence of the parallel block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices |
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| Authors: | Gabriel Okša Yusaku Yamamoto Martin Bečka Marián Vajteršic |
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| Institution: | 1.Institute of Mathematics,Slovak Academy of Sciences,Bratislava,Slovak Republic;2.Department of Communication Engineering and Informatics,The University of Electro-Communications,Tokyo,Japan;3.Department of Computer Sciences,University of Salzburg,Salzburg,Austria |
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| Abstract: | The proof of the asymptotic quadratic convergence is provided for the parallel two-sided block-Jacobi EVD algorithm with dynamic ordering for Hermitian matrices. The discussion covers the case of well-separated eigenvalues as well as clusters of eigenvalues. Having p processors, each parallel iteration step consists of zeroing 2p off-diagonal blocks chosen by dynamic ordering with the aim to maximize the decrease of the off-diagonal Frobenius norm. Numerical experiments illustrate and confirm the developed theory. |
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