Quasi-Laguerre Iteration in Solving Symmetric Tridiagonal Eigenvalue Problems
Qiang Du, Ming Jin, T. Y. Li, Zhonggang Zeng · SIAM Journal on Scientific Computing · 1996
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.