A comparison of conventional acceleration schemes to the method of residual expansion functions

Persistent Link:
http://hdl.handle.net/10150/277176
Title:
A comparison of conventional acceleration schemes to the method of residual expansion functions
Author:
Rustaey, Abid, 1961-
Issue Date:
1989
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The algebraic equations resulting from a finite difference approximation may be solved numerically. A new scheme that appears quite promising is the method of residual expansion functions. In addition to speedy convergence, it is also independent of the number of algebraic equations under consideration, hence enabling us to analyze larger systems with higher accuracies. A factor which plays an important role in convergence of some numerical schemes is the concept of diagonal dominance. Matrices that converge at high rates are indeed the ones that possess a high degree of diagonal dominance. Another attractive feature of the method of residual expansion functions is its accurate convergence with minimal degree of diagonal dominance. Methods such as simultaneous and successive displacements, Chebyshev and projection are also discussed, but unlike the method of residual expansion functions, their convergence rates are strongly dependent on the degree of diagonal dominance.
Type:
text; Thesis-Reproduction (electronic)
Keywords:
Differential equations.; Functions.
Degree Name:
M.S.
Degree Level:
masters
Degree Program:
Graduate College; Nuclear and Energy Engineering
Degree Grantor:
University of Arizona
Advisor:
Filippone, William

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleA comparison of conventional acceleration schemes to the method of residual expansion functionsen_US
dc.creatorRustaey, Abid, 1961-en_US
dc.contributor.authorRustaey, Abid, 1961-en_US
dc.date.issued1989en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe algebraic equations resulting from a finite difference approximation may be solved numerically. A new scheme that appears quite promising is the method of residual expansion functions. In addition to speedy convergence, it is also independent of the number of algebraic equations under consideration, hence enabling us to analyze larger systems with higher accuracies. A factor which plays an important role in convergence of some numerical schemes is the concept of diagonal dominance. Matrices that converge at high rates are indeed the ones that possess a high degree of diagonal dominance. Another attractive feature of the method of residual expansion functions is its accurate convergence with minimal degree of diagonal dominance. Methods such as simultaneous and successive displacements, Chebyshev and projection are also discussed, but unlike the method of residual expansion functions, their convergence rates are strongly dependent on the degree of diagonal dominance.en_US
dc.typetexten_US
dc.typeThesis-Reproduction (electronic)en_US
dc.subjectDifferential equations.en_US
dc.subjectFunctions.en_US
thesis.degree.nameM.S.en_US
thesis.degree.levelmastersen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineNuclear and Energy Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorFilippone, Williamen_US
dc.identifier.proquest1339057en_US
dc.identifier.oclc23379160en_US
dc.identifier.bibrecord.b17622475en_US
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