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On The Use Of Quasi-Newton Methods For The Minimization Of Convex Quadratic Splines, William Howard Thomas Ii
On The Use Of Quasi-Newton Methods For The Minimization Of Convex Quadratic Splines, William Howard Thomas Ii
Mathematics & Statistics Theses & Dissertations
In reformulating a strictly convex quadratic program with simple bound constraints as the unconstrained minimization of a strictly convex quadratic spline, established algorithms can be implemented with relaxed differentiability conditions. In this work, the positive definite secant update method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) is investigated as a tool to solve the unconstrained minimization problem. It is shown that there is a linear convergence rate and, for nondegenerate problems, the process terminates in a finite number of iterations. Numerical examples are provided.
The Computation Of Exact Green's Functions In Acoustic Analogy By A Spectral Collocation Boundary Element Method, Andrea D. Jones
The Computation Of Exact Green's Functions In Acoustic Analogy By A Spectral Collocation Boundary Element Method, Andrea D. Jones
Mathematics & Statistics Theses & Dissertations
Aircraft airframe noise pollution resulting from the take-off and landing of airplanes is a growing concern. Because of advances in numerical analysis and computer technology, most of the current noise prediction methods are computationally efficient. However, the ability to effectively apply an approach to complex airframe geometries continues to challenge researchers. The objective of this research is to develop and analyze a robust noise prediction method for dealing with geometrical modifications. This new approach for determining sound pressure involves computing exact, or tailored, Green's functions for use in acoustic analogy. The effects of sound propagation and scattering by solid surfaces …
A Technique For Solving The Singular Integral Equations Of Potential Theory, Brian George Burns
A Technique For Solving The Singular Integral Equations Of Potential Theory, Brian George Burns
Mathematics & Statistics Theses & Dissertations
The singular integral equations of Potential Theory are investigated using ideas from both classical and contemporary mathematics. The goal of this semi-analytic approach is to produce numerical schemes that are both general and computationally simple. Previous works based on classical methods have yielded solutions only for very special cases while contemporary methods such as finite differences, finite elements and boundary element techniques are computationally extensive. Since the two-dimensional integral equations of interest exhibit structural invariance under a wide class of conformal mappings initial emphasis is placed on circular domains. By Fourier expansion with respect to the angular variable, such two-dimensional …