Browsing Computational and Applied Mathematics by Title
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TimeSplitting Methods for AdvectionDiffusionReaction Equations Arising in Contaminant Transport
(199203)Two timesplitting methods for advectiondiffusionreaction problems are discussed and analyzed. Numerical results for the first approach applied to bioremediation of contaminants in groundwater are presented. 
TimeStepping Classes for Optimization (TSOpt)
(200909)This report introduces the "Time Stepping Package for Optimization", or TSOpt, which is an interface for timestepping simulation written in C++. It packages a simulator together with its derivatives (\sensitivities") and ... 
Topological Schemas of Cognitive Maps and Spatial Learning
(2016)Spatial navigation in mammals is based on building a mental representation of their environmenta cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains ... 
Topological Schemas of Memory Spaces
(2018)Hippocampal cognitive mapa neuronal representation of the spatial environmentis widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a ... 
Toward Direct Sparse Updates of Cholesky Factors
(198304)A very important problem in numerical optimization is to find a way to update a sparse Hessian approximation so that it will be positive definite under reasonable circumstances. This problem has motivated research, which ... 
Trace Regularity for a Second Order Hyperbolic Equation with Nonsmooth Coefficients
(199101)In this research, a trace regularity theorem on a time like surface is proved for the solution of a multidimensional linear acoustic wave equation with nonsmooth coefficients. Our theorem indicates that with microlocal ... 
TracePenalty Minimization for Largescale Eigenspace Computation
(201302)The RayleighRitz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively highdimensional eigenspaces of large sparse matrices. Although operations involved in RR steps can be ... 
Transfer of Approximation and Numerical Homogenization of Hyperbolic Boundary Value Problems with a Continuum of Scales
(201209)Galerkin approximate solutions of two selfadjoint systems with the same righthand side have errors that mutually dominate each other, provided that the approximating subspaces contain exact solutions to problems with the ... 
Transformation and Reparametrization for Best Linear Unbiased Estimation of a Linear Model with Arbitrary Known Variance
(198607)Two approaches to the problem of best linear unbiased estimation and testing of a linear hypothesis in a linear model under known arbitrary variance are presented which lead directly to efficient and numerically stable ... 
Truncated QZ Methods for Large Scale Generalized Eigenvalue Problems
(199802)This paper presents three methods for the large scale generalized eigenvalue problem: Ax = Bx·lambda. These methods are developed within a subspace projection framework as a truncation and modification of the QZalgorithm ... 
Trust Region SQP Methods With Inexact Linear System Solves For LargeScale Optimization
(200603)This thesis extends the design and the global convergence analysis of a class of trustregion sequential quadratic programming (SQP) algorithms for smooth nonlinear optimization to allow for an efficient integration of ... 
Trust, But Verify: Fast and Accurate Signal Recovery from 1bit Compressive Measurements
(201011)The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical ShannonNyquist rate. To date, the CS theory has assumed primarily realvalued measurements; ... 
A TrustRegion Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
(2013)The numerical solution of optimization problems governed by partial differential equations (PDEs) with random coefficients is computationally challenging because of the large number of deterministic PDE solves required at ... 
TrustRegion InteriorPoint SQP Algorithms for a Class of Nonlinear Programming Problems
(199412)In this paper a family of trustregion interiorpoint SQP algorithms for the solution of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such ... 
TwoGrid Methods for Mixed Finite Element Approximations of Nonlinear Parabolic Equations
(199401)Mixed finite element approximation of nonlinear parabolic equations is discussed. The equation considered is a prototype of a model which arises in flow through porous media. A twogrid approximation scheme is developed ... 
Understanding code generated by TAMC
(200006)The Tangent linear and Adjoint Model Compiler (TAMC) is an automatic differentiation package designed and implemented by Ralf Giering. The code generated by TAMC can be understood in terms of a careful mathematical model ... 
User's Guide for LMaFit: Lowrank Matrix Fitting
(200908)This User's Guide describes the functionality and basic usage of the Matlab package LMaFit for lowrank matrix optimization. It also briefly explains the formulations and algorithms used. 
User's Guide For YALL1: Your Algorithms for L1 Optimization
(200905)This User's Guide describes the functionality and basic usage of the Matlab package YALL1 for L1 minimization. The oneforsix algorithm used in the YALL1 solver is briefly introduced in the appendix. 
Using Simplex Gradients of Nonsmooth Functions in Direct Search Methods
(200612)It has been shown recently that the efficiency of direct search methods that use opportunistic polling in positive spanning directions can be improved significantly by reordering the poll directions according to descent ...