Thesis (Ph. D.)--Middle East Technical University, 2004. / Keywords: linear stability, eigenvalue, high speed-viscous flow, Couette flow, Poiseuille flow, QZ algorithm, critical Reynolds number.

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

In the numerous problems of matrix algebra, one finds the problem of determining the eigenvalues of eigenvectors of a matrix quite frequently. The theory and methods leading to the solution of the eigenvalue and eigenvector problem are of considerable interest. The relation between vector spaces, matrices, eigenvalues, and eigenvectors is to be considered in this chapter, with particular concentration directed toward the eigenvalues and eigenvectors shall be developed in the following chapters with detailed examples of the methods.

A RESEARCH REPORT submitted to the Faculty of Science of the University of the Witwatersrand in partial fulfilment of the degree of MASTER OF SCIENCE Johannesburg, Republic of South Africa December1998· / This work is concerned with the Inverse Eigenvalue Problem for ordinary differential equations of the Sturm-Liouville type in the general form --dd ( 7' ()xdll(t\,:rI)) + {(q) x - t\p:(r )} u (A, Xl, = 0, .1' c.r (I :::: .7' S; b. The central problem considered ill this research is the approximate reC011- struction of the unknown coefficient function q(:l') in the Sturm-Liouville equation JOIl Irom a given finite spectral data set ~i(q), for i = 1 : n . A solution is sought using a finite element discretization method. The method works br solving the non-Iinear system arising out of the difference between the eigenvalues A,(q) of the Sturm-Liouville differential equation and the given spectral data ~i(q). Numerical results me presented to illustrate the effectiveness of the discretization method ill question.

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Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.31).

Thesis (Ph. D.)--University of Hong Kong, 1991.

Thesis (M.S.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (December 19, 2006) Vita. Includes bibliographical references.

The problem of this study was to seek a goodness-of-fit index to compare covariance structure matrices based on the distribution of the mean of the logarithms of the eigenvalues.