Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices

<p>In this thesis we look at iterative methods for solving the primal (<strong>A</strong>x = b) and dual (<strong>A</strong><em>^{<strong>T </strong>}</em>y = g) systems of linear equations to approximate the scattering amplitude defined by g<em>^{<strong>T</strong>}</em>x =y<em>^{<strong>T</strong>}</em>b. 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.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2014

Author dc:creator

• Robertson, Amber Sumner

Contributors dc:contributor

• James V. Lambers
• Jeremy Lyle
• Jiu Ding

• iterative solutions
• large sparse matrices
• Numerical Analysis and Computation
• Other Applied Mathematics

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/63

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1071