Quasi-Laguerre iteration in solving symmetric tridiagonal eigenvalue problems. (English) Zbl 0865.65021
Generalizing the Laguerre iteration, which calculates the zeros of a polynomial with real zeros, a quasi-Laguerre iteration is developed. Contrary to the former, it does not require the calculation of the second derivative. It is monotone, globally convergent with convergence rate \(1+\sqrt 2\). Also applications to eigenvalue problems for symmetric tridiagonal matrices are discussed and extensive numerical tests reported.
Reviewer: L.Elsner (Bielefeld)
MSC:
65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
65H05 | Numerical computation of solutions to single equations |
12Y05 | Computational aspects of field theory and polynomials (MSC2010) |
26C10 | Real polynomials: location of zeros |