Mathematics Commons^™

A Proof Of Convergence For The Tridiagonal Ql Algorithm In Floating-Point Arithmetic, James George Sanderson

Mathematics & Statistics ETDs

Numerous routines are available to find the eigenvalues of a real symmetric tridiagonal matrix. Since it is known to converge in exact arithmetic, the tridiagonal QL algorithm with origin shift is widely used. Here we analyze the algorithm in floating-point arithmetic. This analysis suggests two modifications to the EISPACK implementation TQLl that enable one to prove correctness and hence convergence of the routine.

Also, it is known that the implicit and explicit versions of the QL algorithm produce the same results in exact arithmetic. A counter-example to the floating-point analog of this theorem is presented.

An Abstract Matrix Model: The Column Model, Tomas Eufracio Salazar

Mathematics & Statistics ETDs

In this dissertation we introduce an abstract model for matrix theory, The Column Model. We investigate some properties of the special class of partially ordered linear algebras that satisfy the conditions of the Model. We use the order structure of the Model to obtain some results on: idempotents in the Model, nonnegative elements of the Model having nonnegative generalized inverses, factor theorems in the Model and concepts in the Model that are related to the usual notion of eigenvalues of an m-by-m matrix. Since the set of m-by-m matrices belongs to the special class of partially ordered linear algebras satisfying …

A Metric Graph Structure For Information Retrieval, Karl Jerry Melendez

Mathematics & Statistics ETDs

Document retrieval systems accept a user request for information and respond with a list of documents which contain information relevant to the request. When the documents (or abstracts of the documents) are stored in a computer memory, a function can be defined which estimates the semantic distance between documents. If this function together with the set of documents forms a metric space, a graph, which I call a progressive graph, can be constructed to aid the search for the documents with relevant information.

Progressive graphs are studied and the search algorithms which use this graph structure are presented. The search …