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Using High-Precision Arithmetic to Conquer Numerical Error

PDE and Applied Math Seminar

Speaker: David H. Bailey, Lawrence Berkeley Natl. Lab. (retired) and U.C. Davis, Dept. of Computer Science
Location: 3106 MSB
Start time: Thu, May 15 2014, 4:10PM

Reproducibility is emerging as a major issue for highly parallel computing, in much the same way (and for many of the same reasons) that it is emerging as an issue in other fields of science, technology and medicine, namely the growing numbers of cases where other researchers cannot reproduce published results. One key issue in this regard is numerical reproducibility, namely ensuring that a computation gives reasonably reproducible results across different platforms and different implementations of equivalent algorithms. One effective solution, in many cases, is the judicious usage of high-precision arithmetic in numerically sensitive portions of code. This talk will discuss examples of how high-precision arithmetic, properly applied, can remedy numerical reproducibility problems. The speaker will also mention the growing body of applications of very high precision arithmetic (hundreds or thousands of digits), particularly in mathematics and mathematical physics. For example, high-precision numerical computations, when combined with the “PSLQ” integer relation algorithm and advanced numerical techniques, have been used to discover identities and relations not previously known in the mathematical literature, to identify definite integrals that arise in quantum field theory, and to find minimal polynomials that arise in the theory of Poisson potential functions and lattice sums.