Proceedings of the 2007 international workshop on Symbolic-numeric computation
New progress in real and complex polynomial root-finding
Computers & Mathematics with Applications
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In this article, the quasi-Laguerre iteration is established in the spirit of Laguerre's iteration for solving polynomial $f$ with all real zeros. The new algorithm, which maintains the monotonicity and global convergence of the Laguerre iteration, no longer needs to evaluate $f''$. The ultimate convergence rate is $\sqrt{2} + 1$. When applied to approximate the eigenvalues of a symmetric tridiagonal matrix, the algorithm substantially improves the speed of Laguerre's iteration.