The Mathematical Institute, University of Oxford, Eprints Archive

Approximation of the scattering amplitude

Golub, Gene H. and Stoll, Martin and Wathen, A. J. (2007) Approximation of the scattering amplitude. Technical Report. Unspecified. (Submitted)

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Abstract

The simultaneous solution of Ax=b and ATy=g 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 gTx, 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. 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 preconditioners.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1080
Deposited By:Lotti Ekert
Deposited On:07 May 2011 09:01
Last Modified:07 May 2011 09:01

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