Geodesic
Krylov subspace spectral methods for variable-coefficient initial-boundary value problems
Electronic transactions on numerical analysis, Tome 20 (2005), pp. 212-234.

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Summary: This paper presents an alternative approach to the solution of diffusion problems in the variablecoefficient case that leads to a new numerical method, called a Krylov subspace spectral method. The basic idea behind the method is to use Gaussian quadrature in the spectral domain to compute components of the solution, rather than in the spatial domain as in traditional spectral methods. For each component, a different approximation of the solution operator by a restriction to a low-dimensional Krylov subspace is employed, and each approximation is optimal in some sense for computing the corresponding component. This strategy allows accurate resolution of all desired frequency components without having to resort to smoothing techniques to ensure stability.
Classification : 65M12, 65M70, 65D32
Keywords: spectral methods, Gaussian quadrature, variable-coefficient, Lanczos method 
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     author = {Lambers, James V.},
     title = {Krylov subspace spectral methods for variable-coefficient initial-boundary value problems},
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     volume = {20},
     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__20__a2/}
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Lambers, James V. Krylov subspace spectral methods for variable-coefficient initial-boundary value problems. Electronic transactions on numerical analysis, Tome 20 (2005), pp. 212-234. http://geodesic.mathdoc.fr/item/ETNA_2005__20__a2/