The presence of structure in a computational problem can often be exploited and can lead to a more efficient numerical algorithm. In this dissertation, we look at structured numerical problems that arise from applications in wireless communications and machine learning that also impact other areas of scientific computing. In wireless communication system designs, certain structured matrices (frames) need to be generated. The design of such matrices is equivalent to a symmetric inverse eigenvalue problem where the values of the diagonal elements are prescribed. We present algorithms that are capable of generating a larger set of these constructions than previous algorithms. We also discuss the existence of equiangular tight frames---frames that satisfy additional structural properties. Kernel learning is an important class of problems in machine learning. It often relies on efficient numerical algorithms that solve underlying convex optimization problems. In our work, the objective functions to be minimized are the von Neumann and the LogDet Bregman matrix divergences. The algorithm that solves this optimization problem performs matrix updates based on repeated eigendecompositions of diagonal plus rank-one matrices in the case of von Neumann matrix divergence, and Cholesky updates in case of the LogDet Bregman matrix divergence. Our contribution exploits the low-rank representations and the structure of the constraint matrices, resulting in more efficient algorithms than previously known. We also present two specialized zero-finding algorithms where we exploit the structure through the shape and exact formulation of the objective function. The first zero-finding task arises during the matrix update step which is part of the above-mentioned kernel learning application. The second zero-finding problem is for the secular equation; it is equivalent to the computation of the eigenvalues of a diagonal plus rank-one matrix. The secular equation arises in various applications, the most well-known is the divide-and-conquer eigensolver. In our solutions, we build upon a somewhat forgotten zero-finding method by P. Jarratt, first described in 1966. The method employs first derivatives only and needs the same amount of evaluations as Newton's method, but converges faster. Our contributions are the more efficient specialized zero-finding algorithms. / text

Advances in technology have placed a great emphasis on the design of broadband antennas as well as antenna miniaturization to cope with the demands of making electronic and handheld communication devices smaller and more efficient. In this thesis, the design and fabrication of a frequency independent antenna and a narrow-band planar microstrip Balun are presented. An analysis of frequency selective surfaces is also introduced in order to demonstrate their capability to miniaturize antenna thickness. Lastly, s-parameters measurements and efficiency characterization are performed to determine the radiation properties of surface mount chip inductors in order to determine the feasibility of using them as electrically small antennas.Two types of frequency independent antennas are considered due to their planar geometries, the Equiangular and Archimedean spiral antennas. Frequency independent antennas are radiating devices that have frequency independent impedance and pattern properties because their shape is specified only in terms of angles.The Balun is designed to meet the need of a feeding element for the Archimedean spiral antenna. A Balun is a three port device that connects an unbalanced transmission line such as a coaxial line to a balanced feed line such as the one required by two-arm spiral antennas. The Balun discussed in this work is designed to operate at 2.4 GHz with a 200 MHz bandwidth and to transform the antenna input impedance to a 50-ohm reference impedance. The main characteristics from this device that distinguish it from commercially available structures are its low cost, planarity, and compact footprint. The balancing capability of this Balun is shown by the close agreement between the measured and simulated results. Antennas can be potentially miniaturized in the z-direction by replacing the PEC ground plane separated from the antenna by a lambda /4 thick substrate with a frequency selective surface (FSS) structure that allows the ground plane conductor to be in close proximity to the antenna without affecting its radiation performance. The FSS layer operating at 2.4 GHz presented in this thesis is static (not tuned) and thus the overall bandwidth reduces approximately to the bandwidth obtained with the narrow-band Balun.

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No / A compact-size asymmetrical linearly tapered slot antenna required for portable ultra-wideband (UWB) imaging systems is presented. The total antenna size is reduced compared with the conventional linearly tapered slot antenna by using a triangular slot on the left-hand side of the tapered-shaped radiator, whereas introducing a corrugated pattern of cuts on the right side. The antenna operates over a wide bandwidth extending from 3.1 to 10.6 GHz with a maximum gain of 8.5 dBi. Stable radiation patterns are observed across the operational bandwidth, with cross-polarization levels below 20 dB. The realized antenna structure occupies a volume of 35 x 36 x 0.8 mm3, and possesses the essential time domain fidelity needed for UWB imaging applications. (c) 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.