Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices

Author

Amber Sumner Robertson, University of Southern MississippiFollow

Date of Award

Fall 12-2014

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Committee Chair

James V. Lambers

Committee Chair Department

Mathematics

Committee Member 2

Jeremy Lyle

Committee Member 2 Department

Mathematics

Committee Member 3

Jiu Ding

Committee Member 3 Department

Mathematics

Abstract

In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (A^T y = g) systems of linear equations to approximate the scattering amplitude defined by g^Tx =y^Tb. We use a conjugate gradient-like iteration for a unsymmetric saddle point matrix that is contructed so as to have a real positive spectrum. We find that this method is more consistent than known methods for computing the scattering amplitude such as GLSQR or QMR. Then, we use techniques from "matrices, moments, and quadrature" to compute the scattering amplitude without solving the system directly.

Copyright

2014, Amber Sumner Robertson

Recommended Citation

Robertson, Amber Sumner, "Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices" (2014). Master's Theses. 63.
https://aquila.usm.edu/masters_theses/63