In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (AT y = g) systems of linear equations to approximate the scattering amplitude defined by gTx =yTb. 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.
","abstract_html":"<p>In this thesis we look at iterative methods for solving the primal (<strong>A</strong>x = b) and dual (<strong>A</strong><em><sup><strong>T </strong></sup></em>y = g) systems of linear equations to approximate the scattering amplitude defined by g<em><sup><strong>T</strong></sup></em>x =y<em><sup><strong>T</strong></sup></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>","abstract_has_math":false,"creators":["Robertson, Amber Sumner"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["James V. Lambers","Jeremy Lyle","Jiu Ding"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-01T08:00:00Z","date_published":"2014-12-01T08:00:00Z","updated_at":"2026-07-24T05:44:27Z","subjects":["iterative solutions","large sparse matrices","Numerical Analysis and Computation","Other Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/63","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["James V. Lambers","Jeremy Lyle","Jiu Ding"]},{"key":"dc:creator","label":"Author","values":["Robertson, Amber Sumner"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-01-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["iterative solutions","large sparse matrices","Numerical Analysis and Computation","Other Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/63"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (AT y = g) systems of linear equations to approximate the scattering amplitude defined by gTx =yTb. 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.
"]},{"key":"dc:title","label":"Title","values":["Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices"]}]}],"canonical_facts":{"dc:contributor":["James V. Lambers","Jeremy Lyle","Jiu Ding"],"dc:creator":["Robertson, Amber Sumner"],"dc:date.available":["2014-01-01T08:00:00Z"],"dc:description.abstract":["In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (AT y = g) systems of linear equations to approximate the scattering amplitude defined by gTx =yTb. 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.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/63"],"dc:subject":["iterative solutions","large sparse matrices","Numerical Analysis and Computation","Other Applied Mathematics"],"dc:title":["Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:44:27Z"}