The spectral problem associated with the linearization about solitary waves of the generalized fifth-order KdV equation is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. A numerical framework, based on a fast robust shooting algorithm on exterior algebra spaces is introduced. The complete algorithm has several new features, includin...

This note presents a numerical algorithm to solve a class of multi-point boundary value problems (MBVPs). Compared to conventional multiple shooting, the proposed method uses less parameters to exploit advantages of single shooting approaches. Unknown parameters are updated by a two-step algorithm which improves the convergence of parameters over existing one-step algorithm. The main idea of th...

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is...

Large interconnected systems consist of a multitude of subsystems with their own dynamics, but coupled with each other via input-output connections. Each subsystem is typically modelled by ordinary differential equations or differential-algebraic equations. Simulation and optimal control of such systems pose a challenge both with respect to CPU time and memory requirements. We address optimal c...

Title of Document: DETECTING AND CORRECTING ERRORS IN GENOME ASSEMBLIES Poorani Subramanian, Ph.D. 2010 Directed by: Professor James A. Yorke, Department of Mathematics Genome assemblies have various types of deficiencies or misassemblies. This work is aimed at detecting and correcting a type of misassembly that we call Compression/Expansion or CE misassemblies whereby a section of sequence has...

This paper presents a gathering and shooting progressive refinement radiosity method. Our method integrates the iterative process of light energy gathering used in the standard full matrix method and the iterative process of light energy shooting used in the conventional progressive refinement method. As usual, in each iteration, the algorithm first selects the patch which holds the maximum unp...

For the real-time computation of closed-loop controls, guidance methods have been recently developed by the authors which are based on the theory of neighboring extremals and/or the multiple shooting algorithm. Because of their close relationship, these methods have a comparable domain of controllability, i.e., the set of all deviations from the nominal optimal trajectory which can be compensat...

Global illumination research aiming at the photo-realistic image synthesis pushes forward research in computer graphics as a whole. The computation of visually plausible images is time-consuming and far from being realtime at present. A significant part of computation in global illumination algorithms involves repetitive computing of visibility queries. In the thesis, we describe our results in...