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SOLVING A SEQUENCE OF SPARSE compatible systems
"... We describe how to use an upper trapezoidal sparse orthogonal factorization to solve the sequence of sparse compatible systems needed to implement sparse reduced gradient versions of certain nonsimplex activeset LP methods. For reasons of familiarity, we focus on the reduced gradient nonsimplex a ..."
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Cited by 3 (2 self)
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We describe how to use an upper trapezoidal sparse orthogonal factorization to solve the sequence of sparse compatible systems needed to implement sparse reduced gradient versions of certain nonsimplex activeset LP methods. For reasons of familiarity, we focus on the reduced gradient non
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 653 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
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Cited by 633 (38 self)
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considered the special case where D is an overcomplete system consisting of exactly two orthobases, and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex
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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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
Data mules: Modeling a threetier architecture for sparse sensor networks
 IN IEEE SNPA WORKSHOP
, 2003
"... Abstract — This paper presents and analyzes an architecture that exploits the serendipitous movement of mobile agents in an environment to collect sensor data in sparse sensor networks. The mobile entities, called MULEs, pick up data from sensors when in close range, buffer it, and drop off the data ..."
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Cited by 485 (6 self)
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Abstract — This paper presents and analyzes an architecture that exploits the serendipitous movement of mobile agents in an environment to collect sensor data in sparse sensor networks. The mobile entities, called MULEs, pick up data from sensors when in close range, buffer it, and drop off
Stable recovery of sparse overcomplete representations in the presence of noise
 IEEE TRANS. INFORM. THEORY
, 2006
"... Overcomplete representations are attracting interest in signal processing theory, particularly due to their potential to generate sparse representations of signals. However, in general, the problem of finding sparse representations must be unstable in the presence of noise. This paper establishes t ..."
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Cited by 460 (22 self)
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the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system. Considering an ideal underlying signal that has a sufficiently sparse representation, it is assumed that only a noisy version of it can be observed. Assuming further
The Unix TimeSharing System
 Communications of the ACM
, 1974
"... Unix is a generalpurpose, multiuser, interactive operating system for the larger Digital Equipment Corporation PDP11 and the Interdata 8/32 computers. It offers a number of features seldom found even in larger operating systems, including i A hierarchical file system incorporating demountable vol ..."
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Cited by 539 (14 self)
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volumes, ii Compatible file, device, and interprocess I/O, iii The ability to initiate asynchronous processes, iv System command language selectable on a peruser basis, v Over 100 subsystems including a dozen languages, vi High degree of portability. This paper discusses the nature and implementation
Systems Competition and Network Effects
 JOURNAL OF ECONOMIC PERSPECTIVES—VOLUME 8, NUMBER 2—SPRING 1994—PAGES 93–115
, 1994
"... Many products have little or no value in isolation, but generate value when combined with others. Examples include: nuts and bolts, which together provide fastening services; home audio or video components and programming, which together provide entertainment services; automobiles, repair parts and ..."
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Cited by 544 (6 self)
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. This paper and the others in this symposium explore the economics of such systems. Market competition between systems, as opposed to market competition between individual products, highlights at least three important issues: expectations, coordination, and compatibility. A recent wave of research has focused
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 427 (36 self)
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of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 568 (10 self)
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. In contrast, heuristic attempts to sparsely solve such systems – greedy algorithms and thresholding – perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almostspherical sections in Banach space theory, and deviation bounds for the eigenvalues
Results 1  10
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