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
Model reduction for RF MEMS simulation
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
A time-domain Discontinuous Galerkin method for mechanical resonator quality factor computations
Journal of Computational Physics
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We discuss variants of the Jacobi--Davidson method for solving the generalized complex symmetric eigenvalue problem. The Jacobi--Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product in ${\mathbb C}^n$ with an indefinite inner product. The Rayleigh quotient based on this indefinite inner product leads to an asymptotically cubically convergent Rayleigh quotient iteration. Advantages of the method are illustrated by numerical examples. We deal with problems from electromagnetics that require the computation of interior eigenvalues. The main drawback that we experience in these particular examples is the lack of efficient preconditioners.