Browsing Computational and Applied Mathematics by Title
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Nonlinear Programming by Mesh Adaptive Direct Searches
(200510)This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitations dictate a brief description of various key topics be provided ... 
Nonlinear Waveform Inversion with SurfaceOriented Extended Modeling
(201703)This thesis investigates surfaceoriented model extension approach to nonlinear full waveform inversion (FWI). Conventional leastsquares (LS) approach is capable of reconstructing highly detailed models of subsurface. ... 
Nonnormality in Lyapunov Equations
(201605)The singular values of the solution to a Lyapunov equation determine the potential accuracy of the lowrank approximations constructed by iterative methods. Lowrank solutions are more accurate if most of the singular ... 
Nonparametric Mode Estimation for Higher Dimensional Densities
(198311)In this study a family of estimators is developed for local maxima, or modes, of a multivariate probability density function. The mode estimators are computationally feasible iterative optimization procedures utilizing ... 
NormalBoundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems
(199607)This paper proposes an alternate method for finding several Pareto optimal points for a general nonlinear multicriteria optimization problem. Such points collectively capture the tradeoff among the various conflicting ... 
Notes on Combinatorial Optimization
(198710) 
Novel Techniques for the ZeroForcing and pMedian Graph Location Problems
(201705)This thesis presents new methods for solving two graph location problems, the pMedian problem and the zeroforcing problem. For the pmedian problem, I present a branch decomposition based method that finds the best ... 
Numerical Experience with a PolyhedralNorm CDT TrustRegion Algorithm
(199306)In this paper, we study the modification of the CelisDennisTapia trustregion subproblem which is obtained by replacing the l² norm with a polyhedral norm. The polyhedral norm CDT subproblem can be solved using a standard ... 
Numerical method of characteristics for onedimensional blood flow
(2015)Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a onedimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often ... 
Numerical Methods and Applications for Reduced Models of Blood Flow
(201705)The human cardiovascular system is a vastly complex collection of interacting components, including vessels, organ systems, valves, regulatory mechanisms, mi crocirculations, remodeling tissue, and electrophysiological ... 
Numerical Methods for Modeling Atomistic Trajectories with Diffusion SDEs
(200808)The stochastic dynamics of small scale systems are often not known fromﾠa prioriﾠphysical considerations. We present datadriven numerical methods which can be used to approximate the nonlinear stochastic dynamics associated ... 
Numerical Methods for the Simulation of Flow in RootSoil Systems
(199104)We consider the numerical properties of approximation schemes for a model that simulates water transport in rootsoil systems. The model given in this paper is a reformulation of a previously proposed model now defined ... 
Numerical Optimization Using Computer Experiments
(199703)Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivativefree methods. We propose a method for solving such problems that synthesizes ideas from the ... 
Numerical Safeguarded Use of the Implicit Restarted Lanczos Algorithm for Solving Nonlinear Eigenvalue Problems and its Monotonicity Analysis
(199304)In this thesis, we develop an efficient accurate numerical algorithm for evaluating a few of the smallest eigenvalues and their corresponding eigenvectors for large scale nonlinear eigenproblems. The entries of the matrices ... 
Numerical Simulation and Optimal Shape for Viscous Flow by a Fictitious Domain Method
(199408)In this article we discuss the fictitious domain solution of the NavierStokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to ... 
Numerical Solution of Implicitly Constrained Optimization Problems
(200805)Many applications require the minimization of a smooth function f: Rn → R whose evaluation requires the solution of a system of nonlinear equations. This system represents a numerical simulation that must be run to evaluate ... 
Numerical Solutions of Matrix Equations Arising in Model Reduction of LargeScale LinearTimeInvariant Systems
(200909)This thesis presents and analyzes new algorithms for matrix equations arising from model reduction of lineartimeinvariant (LTI) systems. Such systems arise in a variety of areas, especially in circuit simulation. When ... 
Numerical Techniques for the Treatment of Quasistatic Solid Viscoelastic Stress Problems
(199301)For quasistatic stress problems two alternative constitutive relationships expressing the stress in a linear viscoelastic solid body as a linear functional of the strain are derived. In conjunction with the equations of ... 
Numerically Stable and Statistically Efficient Algorithms for Large Scale Exponential Fitting
(201405)The exponential fitting problem appears in diverse applications such as magnetic resonance spectroscopy, mechanical resonance, chemical reactions, system identification, and radioactive decay. In each application, the ...