TY - JOUR T1 - On the Convergence of Diagonal Elements and Asymptotic Convergence Rates for the Shifted Tridiagonal QL Algorithm AU - Er-Xiong Jiang JO - Journal of Computational Mathematics VL - 3 SP - 252 EP - 261 PY - 1985 DA - 1985/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9622.html KW - AB -

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 $\alpha_j$→$λ_j$ where $λ_j$ 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.