QR decomposition and singular value decomposition: least- squares solutions to overdetermined linear systems

Date

3-1990

Degree

Bachelor of Science in Applied Mathematics

College

College of Arts and Sciences (CAS)

Adviser/Committee Chair

Sharon Joy R. Castillo

Abstract

The study aimed to apply two least-squares methods of solutions to overdetermined systems of linear equations: the OR Decomposition and the Singular Value Decomposition. Both algorithms were coded into computer programs using Turbo Pascal version 5.0 language. The efficiency and accuracy of the algorithms were tested by entering nine sets of overdetermined systems into the devised computer programs. Two matrices entered into the OR program turned out to be singular but when executed in the SVD program were able to obtain approximate least-squares solutions. The results revealed that SVD is more accurate than OR Decomposition since its solution vector x for 6 out of 9 overdetermined systems yielded smaller summation of squares of the residual errors than those obtained by the OR Decomposition. Moreover, SVD can also give approximate least-squares solutions to singular matrices where OR fails to give satisfactory results in this respect.

Language

English

Location

UPLB Main Library Special Collections Section (USCS)

Call Number

Thesis

Document Type

Thesis

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