Eigenvalues of Symmetric Tridiagonal Matrices: A Fast, Accurate and Reliable Algorithm
Victor L. Pereyra, Godela Scherer · IMA Journal of Applied Mathematics · 1973
An algorithm is developed for obtaining eigenvalues of real, symmetric, tridiagonal matrices. It combines dynamically Given's method of bisection and the use of Sturm sequences with various acceleration devices. A FORTRAN IV computer implementation of the algorithm was used on ten test matrices found in the literature. The new method is as precise and reliable as the best published program (Kahan & Varah, 1966), it is never slower, and in at least one case is two and half times faster than the Kahan and Varah program.