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333,969
Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos
, 2002
"... We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations suject to uncertain inputs. In particular, we focus on the solution of the Poisson equation with random diffusivity, forcing and boundary conditions. The stochastic input and so ..."
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Cited by 91 (16 self)
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of deterministic equations for each random mode is solved iteratively by a block GaussSeidel iteration technique. Both discrete and continuous random distributions are considered, and convergence is verified in model problems and against Monte Carlo simulations.
Submitted to CMAME
, 2002
"... We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial di®erential equations suject to uncertain inputs. In particular, we focus on the solution of the Poisson equation with random di®usivity, forcing and boundary conditions. The stochastic input and sol ..."
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of deterministic equations for each random mode is solved iteratively by a block GaussSeidel iteration technique. Both discrete and continuous random distributions are considered, and convergence is veri¯ed in model problems and against Monte Carlo simulations.
Downwind GaußSeidel Smoothing for Convection Dominated Problems
, 1993
"... this paper is the presentation of the numbering techniques. If no cycles arise, one gets a perfect ordering for the pointwise GaußSeidel process. This case is discussed in x2. x3 is devoted to the more general case when cycles appear. We present efficient algorithms which combine the numbering with ..."
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Cited by 2 (0 self)
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this paper is the presentation of the numbering techniques. If no cycles arise, one gets a perfect ordering for the pointwise GaußSeidel process. This case is discussed in x2. x3 is devoted to the more general case when cycles appear. We present efficient algorithms which combine the numbering
Cache aware data laying for the GaussSeidel smoother
 In Proceedings of the Tenth Copper Mountain Conference on Multigrid Methods
, 2001
"... Abstract. Feeding the processor with data operands is the bottleneck in many scientific computations. This bottleneck is alleviated by means of caches, small fast memories to keep data. The performance of a memoryintensive computation depends critically on whether most of the data accesses can be p ..."
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Cited by 1 (1 self)
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promising technique as we achieved considerable performance improvements. For example, our data laying experiments with the GaussSeidel smoother resulted in up to 84 % execution time improvements over the parallelogram based blocked implementation of the algorithm.
Iterative decoding of binary block and convolutional codes
 IEEE Trans. Inform. Theory
, 1996
"... Abstract Iterative decoding of twodimensional systematic convolutional codes has been termed “turbo ” (de)coding. Using loglikelihood algebra, we show that any decoder can he used which accepts soft inputsincluding a priori valuesand delivers soft outputs that can he split into three terms: the ..."
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Cited by 600 (43 self)
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: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the loglikelihood domain are given not only for convolutional codes hut also for any linear binary systematic block code. The iteration
A convergence proof for the turbo decoder as an instance of the GaussSeidel iteration
 in IEEE International Symposium on Information Theory
, 2005
"... Abstract — Many previous attempts at analyzing the convergence behavior of turbo and iterative decoding, such as EXIT style analysis [2] and density evolution [3], ultimately appeal to results which become valid only when the block length grows rather large, while still other attempts, such as conne ..."
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Cited by 3 (2 self)
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extraction as an information projection. This paper recognizes turbo decoding as an instance of a GaussSeidel iteration on a particular nonlinear system of equations. This interpretation holds regardless of block length, and allows a connection to existing convergence results for nonlinear block Gauss
Error bounds on block Gauss–Seidel solutions of coupled multiphysics problems
"... Mathematical models in many fields often consist of coupled submodels, each of which describes a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution ..."
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Cited by 2 (0 self)
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techniques for the individual submodels often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss–Seidel fashion. In this study, we derive two a posteriori bounds
Combining Performance Aspects of Irregular GaussSeidel via Sparse Tiling
 in 15th Workshop on Languages and Compilers for Parallel Computing (LCPC
, 2002
"... Finite Element problems are often solved using multigrid techniques. The most time consuming part of multigrid is the iterative smoother, such as GaussSeidel. To improve performance, iterative smoothers can exploit parallelism, intraiteration data reuse, and interiteration data reuse. Current met ..."
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Cited by 25 (12 self)
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Finite Element problems are often solved using multigrid techniques. The most time consuming part of multigrid is the iterative smoother, such as GaussSeidel. To improve performance, iterative smoothers can exploit parallelism, intraiteration data reuse, and interiteration data reuse. Current
ON THE CONVERGENCE OF THE BLOCK NONLINEAR GAUSSSEIDEL METHOD UNDER CONVEX CONSTRAINTS
"... In this paper we state some new convergence results on the minimization version of the blocknonlinear GaussSeidel (GS) method for problems with feasible set defined as the Cartesian product of closed convex sets. First we derive some general properties of the limit points produced by the GS method ..."
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In this paper we state some new convergence results on the minimization version of the blocknonlinear GaussSeidel (GS) method for problems with feasible set defined as the Cartesian product of closed convex sets. First we derive some general properties of the limit points produced by the GS
A Parallel GaussSeidel Algorithm for Sparse power system matrices
 In SuperComputing '94
, 1994
"... We describe the implementation and performance of an efficient parallel GaussSeidel algorithm that has been developed for irregular, sparse matrices from electrical power systems applications. Although, GaussSeidel algorithms are inherently sequential, by performing specialized orderings on sparse ..."
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Cited by 15 (2 self)
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in the last diagonal block using graph coloring techniques. The ordered matrices often have extensive parallelism, while maintaining the strict precedence relationships in the GaussSeidel algorithm. We present timing results for a parallel GaussSeidel solver implemented on the Thinking Machines CM5
Results 1  10
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333,969