Thesis (M.S.)--University of Missouri, School of Mines and Metallurgy, 1931. / The entire thesis text is included in file. Typescript and handwritten by author. Illustrated by author. Title from title screen of thesis/dissertation PDF file (viewed December 3, 2009) Includes bibliographical references (p. 25) and index (p. 26).

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 85-88). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 85-88). Also available on the Internet.

This work is dealing with speeding up the algorithmization of the MCD es- timator for detection of the mean and the covariance matrix of a normally dis- tributed multivariate data contaminated with outliers. First, the main idea of the estimator and its well-known aproximation by the FastMCD algorithm is discussed. The main focus was to be placed on possibilities of a speedup of the iteration step known as C-step while maintaining the quality of the estimations. This proved to be problematic, if not impossible. The work is, therefore, aiming at creating a new implementation based on the C-step and Jacobi method for eigenvalues. The proposed JacobiMCD algorithm is compared to the FastMCD in terms of floating operation count and results. In conclusion, JacobiMCD is not found to be fully equivalent to FastMCD but hints at a possibility of its usage on larger problems. The numerical experiments suggest that the computation can indeed be quicker by an order of magnitude, while the quality of results is close to those from FastMCD in some settings. 1

This project deals with techniques to solve Markov Chains numerically.

Lattice reduction aided techniques have been successfully applied to a wide range of applications. Efficient and robust lattice basis reduction algorithms are valuable. In this thesis, we present an O(n^4 logB) hybrid Jacobi method for lattice basis reduction, where n is the dimension of the lattice and B is the maximum length of the input lattice basis vectors. Building upon a generic Jacobi method for lattice basis reduction, we integrate the size reduction into the algorithm to improve its performance. To ensure the convergence and the efficiency of the algorithm, we introduce a parameter to the Lagrange reduction. To improve the quality of the computed bases, we impose a condition on the size reduction, delay the structure restoration, and include a postprocessing in the hybrid method. Our experiments on random matrices show that the proposed algorithm produces better reduced bases than the well-known LLL algorithm and BKZ 2.0 algorithm, measured by both the orthogonality defect and the condition number of the basis matrix. Moreover, our hybrid method consistently runs faster than the LLL algorithm, although they have the same theoretical complexity. We have also investigated two potential applications of the hybrid method. The application simulations show that the hybrid method can improve the stability of the communication channels for Multi-Input Multi-Output systems, and can partially discover the plain text when attacking the GGH cryptosystem. / Thesis / Doctor of Philosophy (PhD) / Lattice reduction aided techniques have been successfully applied to a wide range of applications. Efficient and robust lattice basis reduction algorithms are valuable. In this thesis, we present an O(n^4 logB) hybrid Jacobi method for lattice basis reduction, where n is the dimension of the lattice and B is the maximum length of the input lattice basis vectors. Our experiments on random matrices show that the proposed algorithm produces better reduced bases than the well-known LLL algorithm and BKZ 2.0 algorithm, measured by both the orthogonality defect and the condition number of the basis matrix. We have also investigated two potential applications in MIMO systems and cryptosystems.