Browsing Computational and Applied Mathematics by Title
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Potential Inversion of the Two Dimensional Plasma Wave Equation
(199208)A layerstripping type method is developed for solving an inverse problem for the two dimensional plasma wave equation where the object is to find the potential given Cauchy data on a timelike surface. The key point of ... 
Practical Compressive Sensing with Toeplitz and Circulant Matrices
(201001)Compressive sensing encodes a signal into a relatively small number of incoherent linear measurements. In theory, the optimal incoherence is achieved by completely random measurement matrices. However, such matrices are ... 
Predicting solvation free energies and thermodynamics in polar solvents and mixtures using a solvationlayer interface condition
(2017)We demonstrate that with two small modifications, the popular dielectric continuum model is capable of predicting, with high accuracy, ion solvation thermodynamics (Gibbs free energies, entropies, and heat capacities) in ... 
Program Analysis and Transformation in Mathematical Programming
(200808)Over the years, mathematical models have become increasingly complex. Rarely can we accurately model a process using only linear or quadratic functions. Instead, we must employ complicated routines written in some programming ... 
Program Specification Testing within an Integrated Programming Environment
(198311)Our research breaks down into three parts. First, we are exploring the mathematical foundations of program specifications and applying the understanding that we gain to the subject of specification language design. The ... 
Programming Language Support for Supercomputers
(198310)To date, programming language research has made several major contributions to the support of high speed computing. First, highly optimizing compilers have permitted the programmer to write in a high level language without ... 
Programming the Nanocell, a Random Array of Molecules
(200205)The emerging field of molecular electronics seeks to create computational function from individual molecules or arrays of molecules. These nanoscale devices would then enable the production of faster, denser, cheaper ... 
Progress in Linear Programming
(199309)There is little doubt that barrier methods are now indispensable tools in the solution of largescale linear programming problems. However, it is our opinion that the results of Lustig, Marsten and Shanno (hereafter LMS) ... 
Projected Newton for the Symmetric Eigenvalue Problem has Order 1+sqrt(2)
(198705)In their study of the classical inverse iteration algorithm, Peters and Wilkinson considered the closely related algorithm that consists of applying Newton's method, followed by a 2norm normalization, to the nonlinear ... 
Projection Methods for Balanced Model Reduction
(200103)The purpose of this paper is to investigate projection methods for the iterative computation of partially balanced reduced order systems. This approach is both completely automatic once an error tolerance is specified and ... 
Projection Pursuit via Multivariate Histograms
(198508)The problem of finding the most interesting lowdimensional subspaces of a multidimensional data set has usually been formulated as a search for the maximum over all projection subspaces of a measure of information. ... 
ProjectionBased Model Reduction in the Context of Optimization with Implicit PDE Constraints
(201705)I use reduced order models (ROMs) to substantially decrease the computational cost of Newton's method for largescale timedependent optimal control problems in settings where solving the implicit constraints and their ... 
Propagation of Singularities and Some Inverse Problems in Wave Propagation
(198909)We review a number of results relating the propagation of singularities for hyperbolic partial differential equations  i.e. the persistence, or nonlocalization, of wave motion  with wellposedness for some inverse problems ... 
Properties of A Class of Preconditioners for Weighted Least Squares Problems
(199904)A sequence of weighted linear least squares problems arises from interiorpoint methods for linear programming where the changes from one problem to the next are the weights and the right hand side. One approach for solving ... 
Pseudospectral Collocation Methods for the Direct Transcription of Optimal Control Problems
(200309)This thesis is concerned with the study of pseudospectral discretizations of optimal control problems governed by ordinary differential equations and with their application to the solution of the International Space Station ... 
PSQR: A Stable and Efficient Penalized Spline Algorithm
(200905)We introduce an algorithm for reliably computing quantities associated with several types of semiparametric mixed models in situations where the condition number on the random effects matrix is large. The algorithm is ... 
Quantifying DNA Melting Transitions Using SingleMolecule Force Spectroscopy
(200809)We stretched a DNA molecule using atomic force microscope and quantified the mechanical properties associated withﾠBandﾠSﾠforms of doublestranded DNA (dsDNA), molten DNA, and singlestranded DNA (ssDNA). We also fit ... 
Quantifying Multiscale Noise Sources in SingleMolecule Time Series
(200809)When analyzing singlemolecule data, a lowdimensional set of system observables typically serve as the observational data. We calibrate stochastic dynamical models from time series that record such observables. Numerical ... 
Quantitative Object Reconstruction using Abel Transform XRay Tomography and Mixed Variable Optimization
(200702)This paper introduces a new approach to the problem of quantitatively reconstructing cylindrically symmetric objects from radiograph data obtained via xray tomography. Specifically, a mixed variable programming (MVP) ... 
QuasiNewton Methods and Galerkin Procedures for Nonlinear Elliptic Boundary Value Problems
(198312)Least change secant update strategies are derived that are compatible with algebraic systems of nonlinear equations arising when Galerkin procedures are applied to nonlinear elliptic boundary value problems. The resulting ...