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341
A comparison of methods for accurate summation
 SIGSAM Bull
, 2004
"... The summation of large sets of numbers is prone to serious rounding errors. Several methods of controlling these errors are compared, with respect to both speed and accuracy. It is found that the method of “Cascading Accumulators ” is the fastest of several accurate methods. The Double Compensation ..."
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Cited by 9 (0 self)
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method (in both single and double precision versions) is also perfectly accurate in all the tests performed. Although slower than the Cascade method, it is recommended when double precision accuracy is required. C programs that implement both these methods are available in the BULLETIN online repository
FGMRES to obtain backward stability in mixed precision
, 2008
"... Dedicated to Gérard Meurant on the occasion of his 60th birthday Abstract. We consider the triangular factorization of matrices in singleprecision arithmetic and show how these factors can be used to obtain a backward stable solution. Our aim is to obtain doubleprecision accuracy even when the sy ..."
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Cited by 11 (2 self)
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Dedicated to Gérard Meurant on the occasion of his 60th birthday Abstract. We consider the triangular factorization of matrices in singleprecision arithmetic and show how these factors can be used to obtain a backward stable solution. Our aim is to obtain doubleprecision accuracy even when
Solving systems of linear equations on the CELL processor using Cholesky factorization
 Trans. Parallel Distrib. Syst
, 2007
"... pioneering solutions in processor architecture. At the same time it presents new challenges for the development of numerical algorithms. One is effective exploitation of the differential between the speed of single and double precision arithmetic; the other is efficient parallelization between the s ..."
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Cited by 37 (27 self)
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the short vector SIMD cores. In this work, the first challenge is addressed by utilizing a mixedprecision algorithm for the solution of a dense symmetric positive definite system of linear equations, which delivers double precision accuracy, while performing the bulk of the work in single precision
HORIZON: Accelerated General Relativistic Magnetohydrodynamics
"... We present HORIZON, a new graphics processing unit (GPU)accelerated code to solve the equations of general relativistic magnetohydrodynamics in a given spacetime. We evaluate the code in several test cases, including magnetized Riemann problems and rapidly rotating neutron stars, and measure the p ..."
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the performance benefits of the GPU acceleration in comparison to our CPUbased code THOR. We find substantial performance gains in comparison to a quadcore CPU both in single and doubleprecision accuracy, and discuss these findings in the context of future numerical modeling efforts. Subject headings
Implementation of the MixedPrecision High Performance
 LINPACK Benchmark on the CELL Processor,” University of Tennessee Computer Science, Tech. Rep. UTCS06580, LAPACK Working Note 177
, 2006
"... This paper describes the design concepts behind implementations of mixedprecision linear algebra routines targeted for the Cell processor. It describes in detail the implementation of code to solve linear system of equations using Gaussian elimination in single precision with iterative refinement o ..."
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Cited by 15 (0 self)
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of the solution to the full double precision accuracy. By utilizing this approach the algorithm achieves close to an order of magnitude higher performance on the Cell processor than the performance offered by the standard double precision algorithm. Effectively the code is an implementation of the high
Implementation of a MixedPrecision in Solving Systems of Linear Equations on the CELL Processor
, 2006
"... This paper describes the design concepts behind implementations of mixedprecision linear algebra routines targeted for the Cell processor. It describes in detail the implementation of code to solve linear system of equations using Gaussian elimination in single precision with iterative refinement o ..."
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Cited by 2 (0 self)
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of the solution to the full double precision accuracy. By utilizing this approach the algorithm achieves close to an order of magnitude higher performance on the Cell processor than the performance offered by the standard double precision algorithm. Effectively the code is an implementation of the high
Mixedprecision GPU Krylov solver for lattice QCD
"... Using the CUDA platform we have implemented a mixed precision Krylov solver for the WilsonDirac matrix for lattice QCD. The matrixvector product which accounts for the vast majority of the operations runs in excess of 130 Gflops in single precision on the GTX 280. We have developed a new approach ..."
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approach for mixedprecision Krylov solvers that achieves in excess of 100 Gflops and achieves full double precision accuracy. We also explore the use of half precision in this context to further decrease time to solution. Finally we report on initial findings for extending the problem tomultiGPUs, where
Efficient timedomain simulation of frequencydependent elements
 IEEE/ ACM International Conference on ComputerAided Design: Digest of Technical Papers
, 1996
"... We describe an efficient algorithm for timedomain simulation of elements described by causal impulse responses. The computational bottleneck in the simulation of such elements is the need to compute convolutions at each time point. Hence, direct approaches for the simulation of such elements requ ..."
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Cited by 8 (1 self)
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require timeO(N 2), where N is the length of the simulation. We apply ideas from approximation theory to reduce this complexity to O(N logN) while maintaining doubleprecision accuracy. The only restriction imposed by our method is that the impulse response h(t) gets “smoother ” as t goes to infinity
Energy Footprint of Advanced Dense Numerical Linear Algebra using Tile Algorithms on Multicore Architecture
"... We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floatingpoint arithmeti ..."
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Cited by 5 (1 self)
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point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving overdetermined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile
Source excitation strategies for obtaining impulse responses in finite difference time domain room acoustics simulation,”
 Appl. Acoust.
, 2014
"... a b s t r a c t This paper considers source excitation strategies in finite difference time domain room acoustics simulations for auralization purposes. We demonstrate that FDTD simulations can be conducted to obtain impulse responses based on unit impulse excitation, this being the shortest, simpl ..."
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Cited by 2 (1 self)
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, simplest and most efficiently implemented signal that might be applied. Single, rather than double, precision accuracy simulations might be implemented where memory use is critical but the consequence is a remarkably increased noise floor. Hard source excitation introduces a discontinuity in the simulated
Results 1  10
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