Computer Science

SCCM

GATES 2B MC 9025

Stanford, CA 94305-9025

`golub@sccm.stan.ed`

`http://www-sccm.stanford.edu/Faculty/Golub.html`

Schlumberger-Sugar Land Product Center

P.O. Box 2175,

Houston, TX 77252-2175

`GMINERBO@sugar-land.anadrill.slb.com`

NCSA

Dept. of Computer Science

University of Illinois, Urbana-Champaign

Urbana, IL 61801

`saylor@cs.uiuc.edu`

`http://www.uiuc.edu/ph/www/p-saylor`

**Abstract:**-
In many situations, scattering problems require computing c^T A^{-1}
b, where the vectors b and c represent the transmitter and receiver,
respectively. Problems of this type arise in acoustics, electromagnetics,
radar, optics, and quantum mechanics. Often A is a complex symmetric
matrix, whose imaginary part is a positive definite matrix. Solving Ax = b
corresponds to computing the field everywhere. Computing c^T A^{-1} b
corresponds to estimating the receiver signal, which should be easier than
finding x accurately everywhere. If x_k is an iterative approximation, c^T
x_k is a straightforward estimate. We shall look at other forms with which
to estimate the received signal and look at formulating c^T x as a
constraint on the solution of Ax = b.
**Keywords:**- Constraint, Bi-Conjugate Gradient Method, inner products, scatterer