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Bounds on the extremal eigenvalues of positive definite matrices.

dc.contributor.advisorSingh, Virath Sewnath.
dc.contributor.advisorSingh, Pravin.
dc.contributor.authorJele, Thokozani Cyprian Martin.
dc.date.accessioned2023-09-14T15:44:45Z
dc.date.available2023-09-14T15:44:45Z
dc.date.created2018
dc.date.issued2018
dc.descriptionMaster’s degree. University of KwaZulu-Natal, Durban.en_US
dc.description.abstractThe minimum and maximum eigenvalues of a positive de nite matrix are crucial to determining the condition number of linear systems. These can be bounded below and above respectively using the Gershgorin circle theorem. Here we seek upper bounds for the minimum eigenvalue and lower bounds for the maximum eigenvalue. Intervals containing the extremal eigenvalues are obtained for the special case of Toeplitz matrices. The theory of quadratic forms is discussed in detail as it is fundamental in obtaining these bounds.en_US
dc.identifier.urihttps://researchspace.ukzn.ac.za/handle/10413/22261
dc.language.isoenen_US
dc.subject.otherEigenvalues.en_US
dc.subject.otherLinear systems.en_US
dc.subject.otherToeplitz matrices.en_US
dc.titleBounds on the extremal eigenvalues of positive definite matrices.en_US
dc.typeThesisen_US

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