Convergence and Comparison Theorems for Various Splittings of Matrices Based on Generalized Inverses

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dc.contributor.advisorGuo, Chun-Hua
dc.contributor.authorAgasthian, Vijayaparvathy
dc.contributor.committeememberArgerami, Martin
dc.contributor.committeememberFallat, Shaun
dc.contributor.committeememberYang, Boting
dc.contributor.externalexaminerWei, Yi-Min
dc.date.accessioned2015-07-22T17:17:16Z
dc.date.available2015-07-22T17:17:16Z
dc.date.issued2015-03
dc.descriptionA thesis submitted to the Faculty of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics, University of Regina. vi, 106 p.en_US
dc.description.abstractThe convergence of iterative methods for numerically solving the linear systems of equations associated with different types of splittings has been well studied in the literature. In this dissertation, we define new types of splittings based on generalized inverses (Moore-Penrose inverse, Drazin inverse, Group inverse) and present convergence results based on those splittings, namely, Weak Nonnegative Proper Splitting, Proper Regular Splitting, Index Proper Regular Splitting, Weak Nonnegative Index Proper Splitting, Group Proper Regular Splitting, and Weak Nonnegative Group Proper Splitting. We also present some new comparison theorems between the spectral radii of matrices, which are useful in the analysis of the rate of convergence of iterative methods for the different types of splittings of matrices.en_US
dc.description.authorstatusStudenten
dc.description.peerreviewyesen
dc.description.uriA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy *, University of Regina. *, * p.en
dc.identifier.tcnumberTC-SRU-5825
dc.identifier.thesisurlhttp://ourspace.uregina.ca/bitstream/handle/10294/5825/Agasthian_Vijayaparvathy_200287953_PhD_Math_Spring2015.pdf
dc.identifier.urihttps://hdl.handle.net/10294/5825
dc.language.isoenen_US
dc.publisherFaculty of Graduate Studies and Research, University of Reginaen_US
dc.titleConvergence and Comparison Theorems for Various Splittings of Matrices Based on Generalized Inversesen_US
dc.typeThesisen
thesis.degree.departmentDepartment of Mathematics and Statisticsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Reginaen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (PhD)en_US
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