Numerical validation of compensated algorithms with stochastic arithmetic
نویسندگان
چکیده
منابع مشابه
Numerical Validation of Compensated Summation Algorithms with Stochastic Arithmetic
Compensated summation algorithms are designed to improve the accuracy of ill-conditioned sums. They are based on algorithms, such as FastTwoSum, which are proved to provide, with rounding to nearest, the sum of two floating-point numbers and the associated rounding error. Discrete stochastic arithmetic enables one to estimate rounding error propagation in numerical codes. It requires a random r...
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Rounding error may totally corrupt the result of a oating point computation.How to improve and validate the accuracy of a oating point computation, without largecomputing time overheads ? We contribute to this question considering two examples:polynomial evaluation and linear triangular system solving. In both cases we use thecompensation of the rounding errors to improve the ac...
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Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-step θ method is proposed to numerically solve the stochastic differential ...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2018
ISSN: 0096-3003
DOI: 10.1016/j.amc.2018.02.004