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...
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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 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.
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