Summary.
A quadratic convergence bound for scaled Jacobi iterates is proved provided the initial symmetric positive definite matrix has simple eigenvalues. The bound is expressed in terms of the off-norm of the scaled initial matrix and the minimum relative gap in the spectrum. The obtained result can be used to predict the stopping moment in the two-sided and especially in the one-sided Jacobi method.
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Received October 31, 1997 / Revised version received March 8, 1999 / Published online July 12, 2000
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Matejaš, J. Quadratic convergence of scaled matrices in Jacobi method. Numer. Math. 87, 171–199 (2000). https://doi.org/10.1007/s002110000167
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DOI: https://doi.org/10.1007/s002110000167