Partial Gauss-Seidel Approach to Solve Large Scale Linear Systems

• Other Authors: Ghadiyali, Huzefa Shabbir (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Industrial engineering
• Online Access: http://purl.flvc.org/fsu/fd/FSU_2016SP_Ghadiyali_fsu_0071N_13280

With the advancement in technology and the constant need for optimization, a lot of resources are directed towards analyzing information collected. This information is in the form of large amounts of data that is gathered at every instant. The analysis of this data is often expressed in the form of linear system equations, where the size of the equations increases proportionally to the size of the data. Many methods have been developed to solve these systems. The main challenge in solving such large systems is to get an accurate solution along with computational eciency. The goal of this thesis is to develop a method which addresses both accuracy and computational eciency in solving large-scale linear systems. Our method will improve existing iterative techniques particularly for a linear equation system i.e. Ax = b where A is a positive denite and sparse full rank matrix. Linear systems of such kinds are commonly found in applications of Spatial regression. Hence, we will be using spatial data available publicly to test our method and present results of our method in this thesis. === A Thesis submitted to the Department of Industrial and Manufacturing Engineering in partial fulfillment of the requirements for the degree of Master of Science. === Spring Semester 2016. === April 1, 2016. === Gauss Seidel method, Iterative methods, linear system, sparse symmetric data, Spatial data === Includes bibliographical references. === Chiwoo Park, Professor Directing Thesis; Abhishek K. Shrivastava, Committee Member; Arda Vanli, Committee Member.