Abstract
It has recently been proved that the Jacobi method for computing eigenvalues and eigenvectors of real symmetric matrices after a certain stage in the process converges quadratically ([3], [4]). The purpose of this paper is to prove that this also applies to the generalization of the Jacobi method for general normal matrices due to Goldstine and Horwitz [2]. We restrict ourselves to the special row cyclic method of enumerating pivot elements, but it is believed that also other kinds of enumeration will give similar results. The proof consists of two parts; in the first part we show that under certain conditions the pivot element chosen is nearly annihilated, and in the second part we use this to study what happens with the off-diagonal elements after a whole sweep has been performed.
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Ruhe, A. On the quadratic convergence of the Jabobi method for normal matrices. BIT 7, 305–313 (1967). https://doi.org/10.1007/BF01939324
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DOI: https://doi.org/10.1007/BF01939324