On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices
Applied Numerical Mathematics
Tridiagonalizing Complex Symmetric Matrices in Waveguide Simulations
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Non-splitting Tridiagonalization of Complex Symmetric Matrices
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
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We present a new fast and efficient algorithm for computing the eigenvalues and eigenvectors of large-size nondefective complex symmetric matrices. Our work was motivated by the emergence of this problem in recent methods for solving chemical reactive problems. The algorithm we present is similiar to the QR (QL) algorithm for complex Hermitian matrices, but we use complex orthogonal (not unitary) transformations. The new algorithm is faster by an order of magnitude than the corresponding EISPACK routine, and is also more amenable for modern parallel and vector supercomputers. We further present improved perturbation bounds for the Householder transformation, which lies at the basis of the whole transformation.