Browsing Computational and Applied Mathematics by Title
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Oil Spill Sensor using Multispectral Infrared Imaging via L1 Minimization
(201011)Early detection of oil spill events is the key to environmental protection and disaster management. Current technology lacks the sensitivity and specificity in detecting the early onset of a smallscale oil spill event. ... 
OKL: A Unified Language for Parallel Architectures
(201506)Rapid evolution of computer processor architectures has spawned multiple programming languages and standards. This thesis strives to address the challenges caused by fast and cyclical changes in programming models. The ... 
On Alternative Problem Formulations for Multidisciplinary Design Optimization
(199212)In this paper we introduce a perspective on multidisciplinary design optimization (MDO) problem formulation that provides a basis for choosing among existing formulations and suggests provocative, new ones. MDO problems ... 
On Characterizing Graphs with Branchwidth at Most Four
(200104)There are several ways in which we can characterize classes of graphs. One such way of classifying graphs is by their brachwidth. In working to characterize the class of graphs with brachwidth at most four beta4 we have ... 
On Convergence of Minimization Methods: Attraction, Repulsion and Selection
(199903)In this paper, we introduce a rather straightforward but fundamental observation concerning the convergence of the general iteration process. x^(k+1) = x^k  alpha(x^k) [B(x^k)]^(1) gradf(x^k) for minimizing a function ... 
On Effectively Computing the Analytic Center of the Solution Set by PrimalDual InteriorPoint Methods
(199508)The computation of the analytic center of the solution set can be important in linear programming applications where it is desirable to obtain a solution that is not near the relative boundary of the solution set. In this ... 
On Eliminating Square Paths in a Square Lattice
(200004)Removing the minimum number of vertices or points from a square lattice such that no square path exists is known as the square path problem. Finding this number as the size of the lattice increases is not so trivial. Results ... 
On Motivating the MitchellTodd Modification of Karmarkar's Algorithm for LP Problems with Free Variables
(199306)In this note, we first observe that the MorshediTapia interpretation of the Karmarkar algorithm naturally offers an extension of the Karmarkar subproblem scaling to problems with free variables. We then note that this ... 
On Numerical Solution of the Maximum Volume Ellipsoid Problem
(200108)In this paper we study practical solution methods for finding the maximumvolume ellipsoid inscribing a given fulldimensional polytope in R n defined by a finite set of affine inequalities. Our goal is to design a ... 
On Secant Updates for Use in General Constrained Optimization
(198409)In this paper we present two new classes of SQP secant methods for the equality constrained optimization problem. One class of methods uses the SQP augmented Lagrangian formulation, while the other class uses the SQP ... 
On Sizing and Shifting the BFGS Update within the Sized Broyden Family of Secant Updates
(199312)Recently Contreras and Tapia demonstrated that selectively sizing the BFGS secant update has numerical value. A conclusion of the current study is that there is numerical value in following a sizing of the BFGS update with ... 
On the Approximation of the Dirichlet to Neumann Map for High Contrast Two Phase Composites
(201304)Many problems in the natural world have high contrast properties, like transport in composites, fluid in porous media and so on. These problems have huge numerical difficulties because of the singularities of their solutions. ... 
On the Approximation of the Dirichlet to Neumann Map for High Contrast Two Phase Composites and its Applications to Domain Decomposition Methods
(201408)My research is concerned with the analysis and numerical simulations of elliptic partial differential equations that model steady state flow (electric, thermal, fluid) in high contrast composite materials consisting of ... 
On the Barzilai and Borwein Choice of Steplength for the Gradient Method
(199005)In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. We derive an interesting relationship between the Barzilai and Borwein gradient method and the shifted power method. ... 
On the Characterization of QSuperlinear Convergence of QuasiNewton InteriorPoint Methods for Nonlinear Programming
(199402)In this paper we extend the wellknown BoggsTolleWang characterization of Qsuperlinear convergence for quasiNewton methods for equality constrained optimization to quasiNewton interiorpoint methods for nonlinear ... 
On the Characterization of Qsuperlinear Convergence of QuasiNewton Methods for Constrained Optimization
(198407)In this paper we present a short, straightforward and selfcontained derivation of the BoggsTolleWang characterization of those quasiNewton methods for equality constrained optimization which produce iterates which are ... 
On the ChiSquaredness of the Quadratic Form {yhat}' V^{yhat}
(198607)In this note we give necessary and sufficient conditions on a symmetric ginverse V^ of V such that the quadratic form {yhat}' V^{yhat} is distributed chisquared, where {yhat} = X{betahat} is the BLUE for X{beta} ... 
On the ComponentWise Convergence Rate
(199806)In this paper we investigate the convergence rate of a sequence of vectors provided that the convergence rates of the components are known. The result of this investigation is then used to study the mstep convergence rate ... 
On the Constants in Inverse Inequalities in L2
(201005)In this paper we determine the constants in multivariate Markov inequalities in the L2norm on an interval, a triangle and a tetrahedron. Using orthonormal polynomials, we derive explicit expression for the constants on ...