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Iterative methods for sparse systems of linear equations with application to guided-wave optics

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Abstract

The large systems of linear equations and linear eigenvalues problems that have to be numerically solved for numerical simulation of wave propagation in optical and microwave circuits can only efficiently be solved with iterative techniques. We briefly review classical methods for eigenproblems as (Shift-and-Invert) power method and Arnoldi’s method. Then we discuss the more recent Jacobi-Davidson method. This method can exploit preconditioning and information from simpler models. We will relate these methods to solvers of linear equations.

© 2001 Optical Society of America

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