Er-Xiong Jiang ¹

The convergence of diagonal elements of an irreducible symmetric triadiagonal matrix under QL algorithm with some kinds of shift is discussed. It is proved that if $\alpha_1-\sigma$-›0 and $\beta_j$-›0, j=1,2,...,m, then $\alpha_j$-›$lambada_j$ where $\lambada_j$ are m eigenvalues of the matrix, and $\sigma$ is the origin shift. The asymptotic convergence rates of three kinds of shift, Rayleigh quotient shift Wilkinson's shift and RW shift, are analysed.

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