"In electronic structure computations, it is necessary to set up and solve a certain nonlinear eigenvalue problem to identify materials. In this dissertation, we first introduce the nonlinear eigenvalue problem and the currently prevailing Self-Consistent Field (SCF) method accelerated by the Anderson acceleration method. We then compare the Anderson acceleration method with the well-known Generalized Minimal Residual (GMRES) method and show that they are essentially equivalent when applied to linear systems. After that, we study a linearly constrained least-squares problem embedded in the Anderson procedure. We use numerical experiments to illustrate the convergence properties. Finally, we give a summary of our work and an outline of future research."

Several conjectured and proven generalizations of the Brouwer Fixed Point Theorem are examined, the plane fixed point problem in particular. The difficulties in proving this important conjecture are discussed. It is shown that it is true when strong additional assumptions are made. Canonical examples are produced which demonstrate the differences between this result and other generalized fixed point theorems.

Several conjectured and proven generalizations of the Brouwer Fixed Point Theorem are examined, the plane fixed point problem in particular. The difficulties in proving this important conjecture are discussed. It is shown that it is true when strong additional assumptions are made. Canonical examples are produced which demonstrate the differences between this result and other generalized fixed point theorems.

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No description available.

This thesis studies implementation-related issues in OFDM-based digital receivers, using the IEEE 802.11a WLAN standard as a specific wireless technology, where the data rate ranges from 6 Mbps to 54 Mbps. Our goal is to expose and exploit the possibility of scaling of the receiver computational complexity in relation to variable data rate requirements. To facilitate such computational scalability, we propose and evaluate the use of the polar coordinates during data processing in the frequency domain. We also evaluate the impact of various fixed-point precision settings during data processing in both the time domain and the frequency domain. We have found that for the 6-Mbps and 54-Mbps data rates the appropriate fixed-point word length should be 15 bits and 20 bits, respectively. While evaluating different fixed-point precision settings, we found that simulations times were prohibitively long. To address this issue, we also propose an alternative 5-step simulation procedure that significantly reduces the simulation time needed to evaluate any given fixed-point setting option. / Graduate

vi, 99 leaves : ill. ; 26 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1974

Thesis (Ph.D.) -- University of Adelaide, Department of Pure Mathematics, 1974.

Thesis--University of Michigan. / Photocopy of typescript. Ann Arbor, Mich. : University Microfilms, 1977. -- 21 cm. Includes bibliographical references (p. 197-200). Also issued in print.

Thesis--University of Michigan. / Photocopy of typescript. Ann Arbor, Mich. : University Microfilms, 1977. -- 21 cm. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (p. 197-200).