Eigenvalues of Symmetric Tridiagonal Matrices: A Fast, Accurate and Reliable Algorithm

An algorithm is developed for obtaining eigenvalues of real,symmetric, tridiagonal matrices. It combines dynamically Given'smethod of bisection and the use of Sturm sequences with variousacceleration devices. A FORTRAN IV computer implementation of the algorithm was usedon ten test matrices found in the literature. The new methodis as precise and reliable as the best published program (Kahan& Varah, 1966), it is never slower, and in at least onecase is two and half times faster than the Kahan and Varah program.