Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Bit-Width Selection for Data-Path Implementations
Proceedings of the 12th international symposium on System synthesis
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
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The selection of predefined analytic grids (partitions of the numeric ranges) to represent input and output functions as histograms has been proposed as a mechanism of approximation in order to control the tradeoff between accuracy and computation times in several areas ranging from simulation to constraint solving. In particular, the application of interval methods for probabilistic function characterization has been shown to have advantages over other methods based on the simulation of random samples. However, standard interval arithmetic has always been used for the computation steps. In this paper, we introduce an alternative approximate arithmetic aimed at controlling the cost of the interval operations. Its distinctive feature is that grids are taken into account by the operators. We apply the technique in the context of probability density functions in order to improve the accuracy of the probability estimates. Results show that this approach has advantages over existing approaches in some particular situations, although computation times tend to increase significantly when analyzing large functions.