Summary
Using a new technique we derive sharp quadratic convergence bounds for the serial symmetric and SVD Jacobi methods. For the symmetric Jacobi method we consider the cases of well and poorely separated eigenvalues. Our result implies the result proposed, but not correctly proved, by Van Kempen. It also extends the well-known result of Wilkinson to the case of multiple eigenvalues.
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This work was supported in part by the U.S. Army. Contract DAAL03-89-C-0038
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Hari, V. On sharp quadratic convergence bounds for the serial Jacobi methods. Numer. Math. 60, 375–406 (1991). https://doi.org/10.1007/BF01385728
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DOI: https://doi.org/10.1007/BF01385728