Thesis(Ph.D.)--Case Western Reserve University, 2010 / Title from PDF (viewed on 2009-12-30) Department of Electrical Engineering and Computer Science Includes abstract Includes bibliographical references and appendices Available online via the OhioLINK ETD Center

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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. September 2014. / A new method of solution to the problem of nding the minimum `1 norm solution to an algebraic underdetermined linear system is developed. The new method is a geometrically clear, primal method. Like some existing methods, the new method can be logically divided into two parts. A number of new techniques are suggested in this part of the algorithm, including an iterative ascent procedure. In the second part of the solution process, the particular solution obtained in the rst part is iteratively improved. We have developed a number of new techniques here corresponding to both single and multi-element exchange procedures. Central to the new method is the development of descent criteria for a direction vector, and the stopping condition.The performance of our algorithm is also compared with two well-known methods from the literature. Our method is shown to be much superior to these well known-methods with respect to both the number of iterations and the wall-clock time required. The iterative computational complexity of the new method also compares favourably with most well-known methods. A geometric heuristic is developed for initial active constraint set selection and a number of theoretical results are given. The heuristic stands to be much more valuable if the results presented herein can be generalised

Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2004. / Verriest, Erik, Committee Member ; Wardi, Yorai, Committee Member ; Yezzi, Anthony, Committee Member ; Wang, Yang, Committee Member ; Egerstedt, Magnus, Committee Chair. Vita. Includes bibliographical references (leaves 80-85).

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Thesis (Ph.D.)--Baylor University, 2007. / Includes bibliographical references (p. 128-130).

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 80-84). Also available via the Internet.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 150-154).

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