@Article{JCM-3-252, author = {}, title = {On the Convergence of Diagonal Elements and Asymptotic Convergence Rates for the Shifted Tridiagonal QL Algorithm}, journal = {Journal of Computational Mathematics}, year = {1985}, volume = {3}, number = {3}, pages = {252--261}, abstract = {

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.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9622.html} }