This paper presents a divide and conquer algorithm for solving the eigenvalue prob-lem of real symmetric band matrices. The new algorithm bases on homotopy con-tinuation, including inverse power iteration and inverse subspace iteration with shift.Numerical results show that our algorithm is strongly competitive with the known algo-rithms in speed. Above all, our algorithm is well suitable for parallel implementation.Numerical results of parallel computing are also presented in this paper.
This paper presents a new divide-and-conquer algorithm for the eigenvalue problem ofsymmtric tridiagonal matrices. The new algorithm bases on bisection and secant iteration,which is different from Cuppen’s method and Laguerre iteration. The results of theoreticalanalysis and numerical testing show that the convergent rate of our algorithm is obviouslyfaster than that of Laguerre iteration presented in [1]. When the problem scale is quite.large, with the same requirement of accuracy, more than 40% of the computing time canbe reduced by using this new algorithm. In the end, we parallelize this new algorithm andget satisfactory testing results.
