Review on stochastic approach to round-off error analysis and its applications

Vignes, Jean

doi:10.1016/0378-4754(88)90070-5

Cited by 27 publications

(11 citation statements)

References 17 publications

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“…Clearly, we cannot expect to see exact zeros, and much discussion has been devoted to the problem of computational zero. We think that the Vignes method [9] is computationally too expensive to be of practical use in our case. A simple and practical criterion for the detection of zeros in the c-table was proposed by Guzinski [10].…”

Section: Blocksmentioning

confidence: 99%

General algorithm of computation of c-table and detection of valleys

Gilewicz¹,

Pindor²

2010

Ukr Math J

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Section: Blocksmentioning

confidence: 99%

General algorithm of computation of c-table and detection of valleys

Gilewicz¹,

Pindor²

2010

Ukr Math J

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“…The discrete stochastic arithmetic (DSA, [7]) is in this category. Comparing to other methods such as lA, rounding error estimation based on the DSA is more effIcient and provides a more realistic knowledge of rounding errors ( [8]).…”

Section: Rounding Error Analysismentioning

confidence: 99%

“…Therefore the computational results can also be modeled by random variables. Based on the probabilistic approach, the DSA has been developed ( [7,9]). It allows estimating the rounding errors on each computational result during the execution of a program.…”

Section: The Discrete Stochastic Arithmeticmentioning

confidence: 99%

“…For this purpose, an efficient method for rounding error estimation on hybrid hardware systems is investigated in this paper. It is based on the discrete stochastic arithmetic (DSA, [7]), and is generally applicable independent of the algorithm. The proposed method can be applied to existing software packages without source code modification.…”

Section: Introductionmentioning

confidence: 99%

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On the numerical sensitivity of computer simulations on hybrid and parallel computing systems

Simon

Kieß

2011

2011 International Conference on High Performance Computing &Amp; Simulation

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Simulation results depend not only on the precision of the floating point arithmetic with respect to the numerical accuracy of the results. They are also sensitive to diff erences of floating point arithmetic implementations of diff erent hybrid and parallel computing systems such as CPUs, GPUs, dedicated processors like the Cell processor or the GRAPE sp ecial-purpose computer with the same precision. As floating point op erations may not maintain basic properties like associative or distributive properties of the underlying mathematical op erations, the numerical values computed by simulations may become dependent on the hardware platform and the sp ecific run of the program. Numerical accuracy control of the simulation would identifY significant variations of the simulation results due to these numerical effects. For this purpose, the numerical accuracy is controlled in this paper by a method for rounding error estimation based on the discrete stochastic arithmetic (DSA). This method, which is investigated on both CPUs and GPUs here, is generally applicable independent of the algorithm and can provide a tight estimation of the rounding errors while increasing the computational time only by a factor of approximately 3 in the ideal case. It is shown that the method can be applied automatically without modifYing source code. Furthermore, performance improvements compared to the numerical accuracy control based on higher precision arithmetic can be obtained.

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“…The CESTAC method was first developed by M. La Porte and J. Vignes [7][8][9][10][11] and was later generalized by the later in [12][13][14][15][16][17][18][19].…”

Section: Basic Ideas Of the Methodsmentioning

confidence: 99%