A fast solver for the complex symmetric eigenproblem1
Abstract
Many numerical methods for studying chemical reaction problems require the computation of the eigenvalues of very large complex symmetric matrices. Recently, a new algorithm for this problem has been proposed by Bar-On and Ryaboy [3]. This algorithm is similar in concept and complexity to the Hermitian eigensolver and is based on application of complex orthogonal transformations to preserve symmetry and recovery transformations to preserve stability. We demonstrate the performance of the proposed algorithm on several high performance computers from Digital, SGI, and Cray. The results show that the new algorithm is much faster than the general eigensolver, the present method used for solving these problems.
References
[2] E. Balslev, J . Combes. Spectral properties of many body Schroedinger operators with dilation analytic interactions. Commun. Math. Phys., 22: 280-294, 1971.
[3] I. Bar-On, V. Ryaboy. Fast diagonalization of large and dense complex symmetric matrices, with applications to quantum reaction dynamics. SIAM J. on Scientific Computing, 18: 1412-1435, 1997.
[4] D. Brown, J . Light. Evaluation of thermal rate constants in the eigenbasis of a Hamiltonian with an optical potential. J. Chern. Phys., 91: 5465- 5471, 1992.
[5] J .K. Cullum, R.A. Willoughby. Lanczos Algorithms for Large Symmetric Eigenvalues Computations. Birkhauser, Boston, 1985.
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