Parallel Bisection Algorithms for Solving the Symmetric Tridiagonal Eigenproblem
نویسندگان
چکیده
In this paper we study the different approaches used so far to apply the bisection method for solving the symmetric tridiagonal eigenproblem. We review the sequential methods used to perform the final extraction of the eigenvalues and compare two new techniques that offer very good results. The sequential version of the bisection method we have implemented even surpasses the results of the QR iteration in some cases. We also perform an exhaustive survey of the approaches that can be used to parallelize the bisection method and we compare two parallel algorithms that apply different schemes for distributing the computation among the processors. The experimental analysis developed shows that the bisection method, besides its flexibility in the partial computation of the spectrum, is a method that offers very good results when it is adequately parallelized. We also show that the behaviour of the algorithms is clearly matrix-dependent.
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