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Modifying CLJP to Select Grid Hierarchies with Lower Operator Complexities and Better Performance ∗
"... Algebraic multigrid (AMG) is an efficient algorithm for solving certain types of large, sparse linear systems. For solving very large problems with AMG it becomes necessary to use parallel algorithms. Coarse grid selection algorithms such as CLJP were created to parallelize the setup phase of AMG. F ..."
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Cited by 2 (2 self)
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Algebraic multigrid (AMG) is an efficient algorithm for solving certain types of large, sparse linear systems. For solving very large problems with AMG it becomes necessary to use parallel algorithms. Coarse grid selection algorithms such as CLJP were created to parallelize the setup phase of AMG
Monte Carlo Localization: Efficient Position Estimation for Mobile Robots
 IN PROC. OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI
, 1999
"... This paper presents a new algorithm for mobile robot localization, called Monte Carlo Localization (MCL). MCL is a version of Markov localization, a family of probabilistic approaches that have recently been applied with great practical success. However, previous approaches were either computational ..."
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Cited by 343 (46 self)
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computationally cumbersome (such as gridbased approaches that represent the state space by highresolution 3D grids), or had to resort to extremely coarsegrained resolutions. Our approach is computationally efficient while retaining the ability to represent (almost) arbitrary distributions. MCL applies sampling
RealTime, Continuous Level of Detail Rendering of Height Fields
, 1996
"... We present an algorithm for realtime level of detail reduction and display of highcomplexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screenspace threshold to bound the maximum error of the projected image. A coarse lev ..."
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Cited by 296 (15 self)
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We present an algorithm for realtime level of detail reduction and display of highcomplexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screenspace threshold to bound the maximum error of the projected image. A coarse
Genetic Algorithms, Noise, and the Sizing of Populations
 COMPLEX SYSTEMS
, 1991
"... This paper considers the effect of stochasticity on the quality of convergence of genetic algorithms (GAs). In many problems, the variance of buildingblock fitness or socalled collateral noise is the major source of variance, and a populationsizing equation is derived to ensure that average sig ..."
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Cited by 276 (85 self)
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This paper considers the effect of stochasticity on the quality of convergence of genetic algorithms (GAs). In many problems, the variance of buildingblock fitness or socalled collateral noise is the major source of variance, and a populationsizing equation is derived to ensure that average
Efficient Setup . . .
, 2007
"... Solving partial differential equations (PDEs) using analytical techniques is intractable for all but the simplest problems. Many computational approaches to approximate solutions to PDEs yield large systems of linear equations. Algorithms known as linear solvers then compute an approximate solution ..."
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constructs a lower dimensional problem to remove error remaining after relaxation. In algebraic multigrid (AMG), the lower dimensional space is constructed by coarsegrid selection algorithms. In this thesis, an introduction and study of independent setbased parallel coarsegrid selection algorithms
Coarsegrid Selection for Parallel Algebraic Multigrid
 Held at Lawrence Berkeley National Laboratory
, 1998
"... . The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG). To date, however, no parallel AMG algorithms exist. We introduce a parallel algorithm for the selection of coarsegrid poin ..."
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Cited by 25 (3 self)
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. The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG). To date, however, no parallel AMG algorithms exist. We introduce a parallel algorithm for the selection of coarsegrid
Computing Geodesic Paths on Manifolds
 Proc. Natl. Acad. Sci. USA
, 1998
"... The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. A ..."
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Cited by 294 (28 self)
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The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity
A greedy strategy for coarsegrid selection
, 2006
"... Efficient solution of the very large linear systems that arise in numerical modelling of realworld applications is often only possible through the use of multilevel techniques. While highly optimized algorithms may be developed using knowledge about the origins of the matrix problem to be considere ..."
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Cited by 10 (4 self)
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to be considered, much recent interest has been in the development of purely algebraic approaches that may be applied in many situations, without problemspecific tuning. Here, we consider an algebraic approach to finding the fine/coarse partitions needed in multilevel approaches. The algorithm is motivated
COARSENING INVARIANCE AND BUCKETSORTED INDEPENDENT SETS FOR ALGEBRAIC MULTIGRID ∗
"... Abstract. Independent setbased coarsegrid selection algorithms for algebraic multigrid are defined by their policies for weight initialization, independent set selection, and weight update. In this paper, we develop theory demonstrating that algorithms employing the same policies produce identical ..."
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Abstract. Independent setbased coarsegrid selection algorithms for algebraic multigrid are defined by their policies for weight initialization, independent set selection, and weight update. In this paper, we develop theory demonstrating that algorithms employing the same policies produce
A cartesian grid method with transient anisotropic adaption
 Journal of Computational Physics
"... A Cartesian grid method with solutionadaptive anisotropic refinement and coarsening is developed for simulating timedependent incompressible flows. The Cartesian grid cells and faces are managed using an unstructured data approach, and algorithms are described for the timeaccurate transient an ..."
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Cited by 17 (2 self)
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the velocity field using a novel approximate factorization technique, although an iterative technique is also presented. The pressure Poisson equation is solved using additive correction multigrid, and an efficient coarse grid selection algorithm is presented. Finally, the Cartesian cell geometry allows
Results 1  10
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1,695