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6,208
Block-relaxation Algorithms in Statistics
, 1994
"... this paper we discuss four such classes of algorithms. Or, more precisely, we discuss a single class of algorithms, and we show how some well-known classes of statistical algorithms fit in this common class. The subclasses are, in logical order, block-relaxation methods augmentation methods majoriza ..."
Abstract
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Cited by 41 (2 self)
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this paper we discuss four such classes of algorithms. Or, more precisely, we discuss a single class of algorithms, and we show how some well-known classes of statistical algorithms fit in this common class. The subclasses are, in logical order, block-relaxation methods augmentation methods
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.
- IEEE Trans. Pattern Anal. Mach. Intell.
, 1984
"... Abstract-We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs di ..."
Abstract
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Cited by 5126 (1 self)
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is a highly parallel "relaxation" algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.
Relaxation Algorithms In Finding Nash Equilibria
- In Computational Economics from Economics Working Paper Archive at WUSTL
, 1997
"... Relaxation algorithms provide a powerful method of finding noncooperative equilibria in general synchronous games. Through use of the NikaidoIsoda function, the Nash solution to a broad category of constrained, multiplayer, non-zerosum games can easily be found. We provide solutions to some simpl ..."
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Relaxation algorithms provide a powerful method of finding noncooperative equilibria in general synchronous games. Through use of the NikaidoIsoda function, the Nash solution to a broad category of constrained, multiplayer, non-zerosum games can easily be found. We provide solutions to some
A Data Locality Optimizing Algorithm
, 1991
"... This paper proposes an algorithm that improves the locality of a loop nest by transforming the code via interchange, reversal, skewing and tiling. The loop transformation algorithm is based on two concepts: a mathematical formulation of reuse and locality, and a loop transformation theory that unifi ..."
Abstract
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Cited by 804 (16 self)
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that unifies the various transforms as unimodular matrix transformations. The algorithm has been implemented in the SUIF (Stanford University Intermediate Format) compiler, and is successful in optimizing codes such as matrix multiplication, successive over-relaxation (SOR), LU decomposition without pivoting
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
Abstract
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Cited by 483 (2 self)
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that has been contaminated with additive noise, the goal is to identify which elementary signals participated and to approximate their coefficients. Although many algorithms have been proposed, there is little theory which guarantees that these algorithms can accurately and efficiently solve the problem
A Multilevel Relaxation Algorithm for Simultaneous Localisation and Mapping
, 2004
"... This paper addresses the problem of simultaneous localisation and mapping (SLAM) by a mobile robot. An incremental SLAM algorithm is introduced that is derived from multigrid methods used for solving partial differential equations. The approach improves on the performance of previous relaxation meth ..."
Abstract
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Cited by 110 (5 self)
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This paper addresses the problem of simultaneous localisation and mapping (SLAM) by a mobile robot. An incremental SLAM algorithm is introduced that is derived from multigrid methods used for solving partial differential equations. The approach improves on the performance of previous relaxation
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
- Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
Abstract
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Cited by 1211 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
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 ..."
Abstract
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Cited by 555 (22 self)
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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
Schwarz Waveform Relaxation Algorithms Laurence Halpern
"... Summary. Optimized Schwarz Waveform Relaxation algorithms have been devel-oped over the last few years for the computation in parallel of evolution problems. In this paper, we present their main features. 1 ..."
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Summary. Optimized Schwarz Waveform Relaxation algorithms have been devel-oped over the last few years for the computation in parallel of evolution problems. In this paper, we present their main features. 1
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