Search results for "round-off error"

showing 4 items of 4 documents

On the propagation of error in certain non-linear algorithms

1959

Computational MathematicsPropagation of uncertaintyNonlinear systemApplied MathematicsNumerical analysisRound-off errorAlgorithmMathematicsNumerische Mathematik
researchProduct

The effect of round-off error on long memory processes

2011

We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both…

Economics and EconometricsDiscretizationGaussianMathematics - Statistics TheoryStatistics Theory (math.ST)long memory processeFOS: Economics and businesssymbols.namesakeStatisticsFOS: MathematicsApplied mathematicsMathematicsHurst exponentStatistical Finance (q-fin.ST)Observational errorQuantitative Finance - Statistical FinanceEstimatordetrended fluctuation analysiround-off errorlong memory processesAutocovariancesymbolsDetrended fluctuation analysisRound-off errorSocial Sciences (miscellaneous)Analysismeasurement errorlocal Whittle estimator
researchProduct

On central algorithms of approximation under fuzzy information

2005

We consider the problem of approximation of an operator by information described by n real characteristics in the case when this information is fuzzy. We develop the well-known idea of an optimal error method of approximation for this case. It is a method whose error is the infimum of the errors of all methods for a given problem characterized by fuzzy numbers in this case. We generalize the concept of central algorithms, which are always optimal error algorithms and in the crisp case are useful both in practice and in theory. In order to do this we define the centre of an L-fuzzy subset of a normed space. The introduced concepts allow us to describe optimal methods of approximation for lin…

Mathematical optimizationFuzzy classificationArtificial IntelligenceLogicApproximation errorFuzzy setFuzzy set operationsFuzzy numberApproximation algorithmRound-off errorAlgorithmFuzzy logicMathematicsFuzzy Sets and Systems
researchProduct

Influence of rounding errors on the quality of heuristic optimization algorithms

2011

Abstract Search space smoothing and related heuristic optimization algorithms provide an alternative approach to simulated annealing and its variants: while simulated annealing traverses barriers in the energy landscape at finite temperatures, search space smoothing intends to remove these barriers, so that a greedy algorithm is sufficient to find the global minimum. Several formulas for smoothing the energy landscape have already been applied, one of them making use of the finite numerical precision on a computer. In this paper, we thoroughly investigate the effect of finite numerical accuracy on the quality of results achieved with heuristic optimization algorithms. We present computation…

Statistics and ProbabilityMathematical optimizationHeuristic (computer science)Simulated annealingRound-off errorCondensed Matter PhysicsGreedy algorithmTravelling salesman problemMetaheuristicGlobal optimizationSmoothingMathematicsPhysica A: Statistical Mechanics and its Applications
researchProduct