Browsing Computational and Applied Mathematics by Title
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Adaptive Finite Element Methods for LinearQuadratic Convection Dominated Elliptic Optimal Control Problems
(200908)The numerical solution of linearquadratic elliptic optimal control problems requires the solution of a coupled system of elliptic partial differential equations (PDEs), consisting of the socalled state PDE, the adjoint ... 
An adaptive multiscale algorithm for efficient extended waveform inversion
(2017)Subsurfaceoffset extended fullwaveform inversion (FWI) may converge to kinematically accurate velocity models without the lowfrequency data accuracy required for standard datadomain FWI. However, this robust alternative ... 
An Algebraic Exploration of Dominating Sets and Vizing's Conjecture
(2012)Systems of polynomial equations are commonly used to model combinatorial problems such as independent set, graph coloring, Hamiltonian path, and others. We formulate the dominating set problem as a system of polynomial ... 
Algorithms for Solving Sparse Nonlinear Systems of Equations
(198604)In this thesis, we present four algorithms for solving sparse nonlinear systems of equations: the partitioned secant algorithm, the CMsuccessive displacement algorithm, the modified CMsuccessive displacement algorithm ... 
Algorithms to Find the Girth and Cogirth of a Linear Matroid
(201511)In this thesis, I present algorithms to find the cogirth and girth, the cardinality of the smallest cocircuit and circuit respectively, of a linear matroid. A set covering problem (SCP) formulation of the problems is ... 
All Stationary Points of Differential Semblance Are Asymptotic Global Minimizers: Layered Acoustics
(1999)Differential semblance velocity estimators have welldefined and smooth high frequency asymptotics. A version appropriate for analysis of CMP gathers and layered acoustic models has no secondary minima. Its structure ... 
Alternating Direction Algorithms for L1Problems in Compressive Sensing
(200911)In this paper, we propose and study the use of alternating direction algorithms for several L1norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, ... 
Alternating Direction Augmented Lagrangian Methods for Semidefinite Programming
(200912)We present an alternating direction method based on an augmented Lagrangian framework for solving semidefinite programming (SDP) problems in standard form. At each iteration, the algorithm, also known as a twosplitting ... 
An Abstract Analysis of Differential Semblance Optimization
(199404)Differential Semblance Optimization (DSO) is a novel way of approaching a class of inverse problems arising in exploration seismology. The promising feature of the DSO method is that it replaces a nonsmooth, highly nonconvex ... 
An accelerated Poisson solver based on multidomain spectral discretization
(2018)This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The method works best for domains that can readily be mapped onto a rectangle, or a ... 
An Adaptive Finite Difference Method for Traveltime and Amplitude
(1999)The eikonal equation with point source is difficult to solve with high order accuracy because of the singularity of the solution at the source. All the formally high order schemes turn out to be first order accurate without ... 
An Algorithmic Characterization of Antimatroids
(198712)In an article entitled "Optimal sequencing of a single machine subject to precedence constraints," E.L. Lawler presented a now classical minmax result for job scheduling. In essence, Lawler's proof demonstrated that the ... 
An Almost LinearTime Algorithm for Graph Realization
(198503)Given a {0,1}matrix M, the graph realization problem for M is to find a tree such that the columns of M are incidence vectors of paths in T, or to show that no such T exists. An algorithm is presented for this problem ... 
An Alternating Direction Algorithm for Matrix Completion with Nonnegative Factors
(201101)This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to nd nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates ... 
An Alternating Direction Algorithm for Nonnegative Matrix Factorization
(201001)We extend the classic alternating direction method for convex optimization to solving the nonconvex, non negative matrix factorization problem and conduct several carefully designed numerical experiments to compare the ... 
An alternating direction and projection algorithm for structureenforced matrix factorization
(2017)Structureenforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning ... 
An Alternating Direction and Projection Algorithm for Structureenforced Matrix Factorization
(201310)Structureenforced matrix factorization (SeMF) represents a large class of mathematical models ap pearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning ... 
An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients
(201204)In this thesis, I develop and analyze a general theoretical framework for optimization problems governed by partial differential equations (PDEs) with random inputs. This theoretical framework is based on the adjoint ... 
An Efficient Algorithm for Calculating the Heat Capacity of a Largescale Molecular System
(200102)We present an efficient algorithm for computing the heat capacity of a largescale molecular system. The new algorithm is based on a special Gaussian quadrature whose abscissas and weights are obtained by a simple Lanczos ... 
An Efficient Augmented Lagrangian Method with Applications to Total Variation Minimization
(201207)Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equalityconstrained nonsmooth optimization problems (chiefly but not necessarily convex programs) ...