Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Nonnegative matrices have a myriad of applications in the biological, social, and physical genres. Of particular importance are the primitive matrices. A nonnegative matrix, M, is primitive exactly when there is a positive integer, k, such that M[superscript k] has only positive entries; that is, all the entries in M[superscript k] are strictly greater than zero. This method of determining if a matrix is primitive uses matrix multiplication and so would require time ���(n[superscipt ��]) where ��>2.3 even if fast matrix multiplication were used. Our goal is to find a much faster algorithm. This can be achieved by viewing a nonnegative matrix, M, as the adjacency matrix for a graph, G(M). The matrix, M, is primitive if and only if G(M) is strongly connected and the greatest common divisor of the cycle lengths in G(M) is 1. We devised an algorithm based in breadth-first search which finds a set of cycle lengths whose gcd is the same as that of G(M). This algorithm has runtime O(e) where e is the number of nonzero entries in M and therefore equivalent to the number of edges in G(M). A proof is given shown the runtime of O(n + e) along with some empirical evidence that supports this finding. / Graduation date: 2003

In this work, we first introduce a novel approach to the long term irrigation scheduling using Genetic Algorithms (GAs). We explore the effectiveness of GAs in the context of optimizing nonlinear crop models and describe application requirements and implementation of the technique. GAs were found to converge quickly to near-optimal solutions. Second, we analyze the relationship between GA control parameters (population size, crossover rate, and mutation rate) and performance. We identify a combination of population, mutation, and crossover which searched the fitness landscape efficiently. The results suggest that smaller populations are able to provide better performance at relatively low mutation rates. More stable outcomes were generated using low mutation rates. Without crossover the quality of solutions were generally impaired, and the search process was lengthened. Aside from crossover rate zero, no other crossover rates significantly differed. The behaviors observed for best, online, offline, and average performances were sensitive to the combined influences control parameters. Interaction among control parameters was strongly indicated. Finally, several adaptive penalty techniques are presented for handling constraints in GAs, and their effectiveness is demonstrated. The constant penalty function suffered from sensitivity to settings of penalty coefficients, and was not successful in satisfying constraints. The adaptive penalty functions utilizes violation distance based metrics and search time based scaling using generation or trials number, and fitness values to penalize infeasible solutions, as the distance from the feasible region or number of generations increases so does the penalty. They were quite successful in providing solutions with minimal effort. They adapt the penalty as the search continues, encouraging feasible solutions to emerge over the time. Adaptive approaches presented here are flexible, efficient, and robust to parameter settings. / Graduation date: 1997

Thesis (M.S.)--Brigham Young University. Dept. of Computer Science, 2006. / Includes bibliographical references (p. 39-41).

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

There are many applications and problems in science and engineering that require large-scale numerical simulations and computations. The issue of choosing an appropriate method to solve these problems is very common, however it is not a trivial one, principally because this decision is most of the times too hard for humans to make, or certain degree of expertise and knowledge in the particular discipline, or in mathematics, are required. Thus, the development of a methodology that can facilitate or automate this process and helps to understand the problem, would be of great interest and help. The proposal is to utilize various statistically based machine-learning and data mining techniques to analyze and automate the process of choosing an appropriate numerical algorithm for solving a specific set of problems (sparse linear systems) based on their individual properties.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 167-176).

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.