Volume 31, pp. 178-203, 2008.
Approximation of the scattering amplitude and linear systems
Gene H. Golub, Martin Stoll, and Andy Wathen
Abstract
The simultaneous solution of and , where 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 , a widely used quantity in signal processing for
example, has a close connection to the above problem since represents the
solution of the forward problem and is the right-hand side of the adjoint
system. We show how this quantity can be efficiently approximated using Gauss
quadrature and introduce a block-Lanczos process that approximates the
scattering amplitude, and which can also be used with preconditioning.
Full Text (PDF) [337 KB],
BibTeX
Key words
Linear systems, Krylov subspaces, Gauss quadrature, adjoint systems.
AMS subject classifications
65F10, 65N22, 65F50, 76D07.
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