NUMERICAL CALCULATION WITH ARBITRARY PRECISION

Numerical Calculation With Arbitrary Precision

The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and rounding errors may induce the user to incorrect interpretation of his/hers answer. In this work, we have developed a computational package to minimize this kin...

Numerical integration in arbitrary-precision ball arithmetic

We present an implementation of arbitrary-precision numerical integration with rigorous error bounds in the Arb library. Rapid convergence is ensured for piecewise complex analytic integrals by use of the Petras algorithm, which combines adaptive bisection with adaptive Gaussian quadrature where error bounds are determined via complex magnitudes without evaluating derivatives. The code is gener...

Sampling with arbitrary precision

We study the problem of the generation of a continuous random variable when a source of independent fair coins is available. We first motivate the choice of a natural criterion for measuring accuracy, the Wasserstein L∞ metric, and then show a universal lower bound for the expected number of required fair coins as a function of the accuracy. In the case of an absolutely continuous random variab...

Intégration numérique avec erreur bornée en précision arbitraire. (Arbitrary precision numerical integration with bounded error)

BOAT: a cross-platform software for data analysis and numerical computing with arbitrary-precision

BOAT is a free cross-platform software for statistical data analysis and numerical computing. Thanks to its multiple-precision floating point engine, it allows arbitrary-precision calculations, whose digits of precision are only limited by the amount of memory of the host machine. At the core of the software is a simple and efficient expression language, whose use is facilitated by the assisted...