Matrix analysis
A QL Procedure for Computing the Eigenvalues of Complex Symmetric Tridiagonal Matrices
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1
A Jacobi--Davidson Method for Solving Complex Symmetric Eigenvalue Problems
SIAM Journal on Scientific Computing
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 discuss a method for solving complex symmetric(non-Hermitian) eigenproblems Ax= ï戮驴Bxarising in an application from optoelectronics, where reduced accuracy requirements provide an opportunity for trading accuracy for performance. In this case, the objective is to exploit the structural symmetry. Consequently, our focus is on a non-Hermitian tridiagonalization process. For solving the resulting complex symmetric tridiagonal problem, a variant of the Lanczos algorithm is used. Based on Fortran implementations of these algorithms, we provide extensive experimental evaluations. Runtimes and numerical accuracy are compared to the standard routine for non-Hermitian eigenproblems, LAPACK/zgeev. Although the performance results reveal that more work is needed in terms of increasing the fraction of Level 3 Blasin our tridiagonalization routine, the numerical accuracy achieved with the non-Hermitian tridiagonalization process is very encouraging and indicates important research directions for this class of eigenproblems.