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102,031
Identification of Sparse Operators
"... Numerical examples, computational complexity and possible applications to other hyperbolic equations or systems, including time dependent problems, will be discussed. All references are available at www.math.tamu.edu/∼popov/preprints.html ..."
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Numerical examples, computational complexity and possible applications to other hyperbolic equations or systems, including time dependent problems, will be discussed. All references are available at www.math.tamu.edu/∼popov/preprints.html
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
, 2007
"... Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined with a spa ..."
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Cited by 539 (17 self)
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sparsenessinducing (ℓ1) regularization term.Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution, and compressed sensing are a few wellknown examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound
Sparse Reconstruction by Separable Approximation
, 2007
"... Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution and reconstruction, and compressed sensing ..."
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Cited by 373 (38 self)
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Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), waveletbased deconvolution and reconstruction, and compressed sensing
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
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Cited by 773 (23 self)
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We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 555 (22 self)
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remarkable features making this attractive for lowrank matrix completion problems. The first is that the softthresholding operation is applied to a sparse matrix; the second is that the rank of the iterates {X k} is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal
Large steps in cloth simulation
 SIGGRAPH 98 Conference Proceedings
, 1998
"... The bottleneck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particle ..."
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Cited by 576 (5 self)
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particles with an implicit integration method. The simulator models cloth as a triangular mesh, with internal cloth forces derived using a simple continuum formulation that supports modeling operations such as local anisotropic stretch or compression; a unified treatment of damping forces is included
Laplacian eigenmaps and spectral techniques for embedding and clustering.
 Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
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Cited by 668 (7 self)
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of the manifold on which the data may possibly reside. Recently, there has been some interest (Tenenbaum et aI, 2000 ; The core algorithm is very simple, has a few local computations and one sparse eigenvalu e problem. The solution reflects th e intrinsic geom etric structure of the manifold. Th e justification
SPARSKIT: a basic tool kit for sparse matrix computations  Version 2
, 1994
"... . This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boei ..."
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Cited by 314 (22 self)
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/Boeing collection of matrices for which we provide a number of tools. Among other things the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, performing basic linear algebra operations with sparse matrices and so on. Work done partly
Linear Algebra Operators for GPU Implementation of Numerical Algorithms
 ACM Transactions on Graphics
, 2003
"... In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for ..."
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Cited by 324 (9 self)
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for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism
Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit
, 2006
"... Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our pr ..."
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Cited by 274 (22 self)
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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our
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