Browsing CAAM Technical Reports by Issue Date
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Application of Harmonic Coordinates to 2D Interface Problems on Regular Grids
(201206)Finite difference and finite element methods exhibit first order convergence when applied to static interface problems where the grid and interface are not aligned. Although modified and unstructured grid methods would ... 
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 ... 
PenaltyFree Discontinuous Galerkin Methods for Incompressible NavierStokes Equations
(201204)A firstorder discontinuous Galerkin method is proposed for solving the steadystate incompressible NavierStokes equations. The stability of this penaltyfree method is obtained by locally enriching the discrete space ... 
Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions
(201203)In many dataintensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations ... 
Decentralized Jointly Sparse Optimization by Reweighted Lq Minimization
(201202)A set of vectors (or signals) are jointly sparse if their nonzero entries are commonly supported on a small subset of locations. Consider a network of agents which collaborative recover a set of joint sparse vectors. This ... 
StructurePreserving Model Reduction of Passive and QuasiActive Neurons
(201201)The spatial component of input signals often carries information crucial to a neuron's function, but models which map synaptic inputs to the transmembrane potential can be computationally expensive. Existing reduced models ... 
Augmented L1 and NuclearNorm Models with a Globally Linearly Convergent Algorithm
(201201)This paper studies the models of minimizing $x_1+1/(2\alpha)x_2^2$ where $x$ is a vector, as well as those of minimizing $X_*+1/(2\alpha)X_F^2$ where $X$ is a matrix and $X_*$ and $X_F$ are the ... 
Learning Circulant Sensing Kernels
(201201)In signal acquisition, Toeplitz and circulant matrices are widely used as sensing operators. They correspond to discrete convolutions and are easily or even naturally realized in various applications. For compressive ... 
Ritz Value Localization for NonHermitian Matrices
(201201)RayleighRitz eigenvalue estimates for Hermitian matrices obey Cauchy interlacing, which has helpful implications for theory, applications, and algorithms. In contrast, few results about the Ritz values of nonHermitian ... 
Error Forgetting of Bregman Iteration
(201201)This short article analyzes an interesting property of the Bregman iterative procedure for minimizing a convex piecewise linear function J(x) subject to linear constraints Ax=b. The procedure obtains its solution by solving ... 
Compressive Sensing for 3D Data Processing Tasks: Applications, Models and Algorithms
(201112)Compressive sensing (CS) is a novel sampling methodology representing a paradigm shift from conventional data acquisition schemes. The theory of compressive sensing ensures that under suitable conditions compressible signals ... 
Ritz Values of Normal Matrices and Ceva's Theorem
(201112)The Cauchy interlacing theorem for Hermitian matrices provides an indispensable tool for understanding eigenvalue estimates and various numerical algorithms that rely on the Ritz values of a matrix. No generalization of ... 
ShortTerm Recurrence Krylov Subspace Methods for NearlyHermitian Matrices
(201110)The Progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residualminimizing shortrecurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a lowrank ... 
LowRank Matrix Recovery using Unconstrained SmoothedLq Minimization
(201109)A lowrank matrix can be recovered from a small number of its linear measurements. As a special case, the matrix completion problem aims to recover the matrix from a subset of its entries. Such problems share many common ... 
Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging
(201109)This paper presents two fast algorithms for total variationbased image reconstruction in partially parallel magnetic resonance imaging (PPI) where the inversion matrix is large and illconditioned. These algorithms utilize ... 
The Stability of GMRES Convergence, with Application to Approximate Deflation Preconditioning
(201109)How does GMRES convergence change when the coefficient matrix is perturbed? Using spectral perturbation theory and resolvent estimates, we develop simple, general bounds that quantify the lag in convergence such a perturbation ... 
TimeDependent Coupling of NavierStokes and Darcy Flows
(201109)A weak solution of the coupling of timedependent NavierStokes equations with Darcy equations is defined. The interface conditions include the BeaversJosephSaffman condition. Existence and uniqueness of the weak solution ... 
Compressive Sensing Based High Resolution Channel Estimation for OFDM System
(201108)Orthogonal frequency division multiplexing (OFDM) is a technique that will prevail in the next generation wireless communication. Channel estimation is one of the key challenges in OFDM, since highresolution channel ... 
Nonlinear Model Reduction via Discrete Empirical Interpolation
(201107)This thesis proposes a model reduction technique for nonlinear dynamical systems based upon combining Proper Orthogonal Decomposition (POD) and a new method, called the Discrete Empirical Interpolation Method (DEIM). The ...