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Thesis (Ph.D.). / Written for the School of Computer Science. Title from title page of PDF (viewed 2008/03/12). Includes bibliographical references.

Thesis (M.S.)--West Virginia University, 2009. / Title from document title page. Document formatted into pages; contains vi, 51 p. : ill. Includes abstract. Includes bibliographical references.

Thesis (M.A.) -- Central Connecticut State University, 2006. / Thesis advisor: Yuanquian Chen. "... in partial fulfillment of the requirements for the degree of Master of Art in Mathematics." Includes bibliographical references (leaf 43). Also available via the World Wide Web.

Zugl.: Bielefeld, Universiẗat, Diss., 1994.

Thesis (M.A.)--Boston University / This paper, utilizing the properties of Vector spaces, describes an approach to polynomial approximations of functions defined analytically or by a set of observations over some interval. If the function and its approximation are both considered tobe elements of a linear normed vector space, a weighted sum or integral of the square of the discrepancy between the function and its approximation is to be a minimum. When this condition is satisfied, and depending upon the interval of interest, the polynomial approximation to the function becomes either the Legendre, Chebyshev, Laguerre, or hermite approximation formulas. An investigation into the properties and applications of these formulas is included, and it is shown that these formulas give the best polynomial approximations to certain functions in the sense of least squares.

A spline function of degree k with knots S₀, S₁,...,Sr is a C[superscript]k-1 function which is a polynomial of degree at most k in each of the intervals (-∞, S₀), (S₀, S₁),…, (Sr,+∞). The Gauss-Markoff Theorem can be used to estimate by least squares the coefficients of a spline function of given degree and knots. Estimating a spline function of known knots without full knowledge of the degree entails an extension of the Gauss-Markoff technique. The estimation of the degree when the knots are also unknown has a possible solution in a method employing finite differences. The technique of minimizing sums of squared residuals forms the basis for a method of estimating the knots of a spline function of given degree. Estimates for the knots may also be obtained by a method of successive approximation, provided additional information about the spline function is known. / Science, Faculty of / Mathematics, Department of / Graduate

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Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard 1 l -minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of simulation results strongly confirming the utility of their approach, they did not rigorously establish the convergence properties of their algorithm. In this paper, we introduce prior information on the support of the sparse domain of the solution into the algorithm of Daubechies et al. We then provide a rigorous proof of the convergence of the resulting algorithm.

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