Victor Pan and Elliot Linzer
We present new algorithms that accelerate the bisection method for the symmetric tridiagonal eigenvalue problem. The algorithms rely on some new techniques, including a new variant of Newton's iteration that reaches cubic convergence (right from the start) to the well separated eigenvalues and can be further applied to acceleration of some other iterative processes, in particular, of the divide-and-conquer methods for the symmetric tridiagonal eigenvalue problem.