Geodesic
Approximation of the scattering amplitude and linear systems
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 178-203
The simultaneous solution of Ax = b and AT y = g, where A is a non-singular matrix, is required in a number of situations. Darmofal and Lu have proposed a method based on the Quasi-Minimal Residual algorithm (QMR). We will introduce a technique for the same purpose based on the LSQR method and show how its performance can be improved when using the generalized LSQR method. We further show how preconditioners can be introduced to enhance the speed of convergence and discuss different preconditioners that can be used. The scattering amplitude gT x, a widely used quantity in signal processing for example, has a close connection to the above problem since x represents the solution of the forward problem and g is the right-hand side of the adjoint system.
Classification : 65F10, 65N22, 65F50, 76D07
Keywords: linear systems, Krylov subspaces, Gauss quadrature, adjoint systems 
@article{ETNA_2008__31__a11,
     author = {Golub,  Gene H. and Stoll,  Martin and Wathen,  Andy},
     title = {Approximation of the scattering amplitude and linear systems},
     journal = {Electronic transactions on numerical analysis},
     pages = {178--203},
     year = {2008},
     volume = {31},
     zbl = {1188.65032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a11/}
}
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%A Stoll,  Martin
%A Wathen,  Andy
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%J Electronic transactions on numerical analysis
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%P 178-203
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%F ETNA_2008__31__a11
Golub,  Gene H.; Stoll,  Martin; Wathen,  Andy. Approximation of the scattering amplitude and linear systems. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 178-203. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a11/