An Efficient Tridiagonal Eigenvalue Solver

In this paper, we propose an algorithm for finding eigenvalues of symmetric tridiagonal matrices based on Laguerre''s iteration. The algorithm is fully parallelizable and has been parallelized on CM5 at University of California at Berkeley. We''ve achieved best possible speedup when matrix dimension is large enough. Besides, we have a well-written serial code which works very efficient in pathologically close eigenvalue cases.