Motivations for an arbitrary precision interval arithmetic and the MPFI library. (English) Zbl 1078.65543

Summary: This paper justifies why an arbitrary precision interval arithmetic is needed. To provide accurate results, interval computations require small input intervals; this explains why bisection is so often employed in interval algorithms. The MPFI library has been built in order to fulfill this need. Indeed, no existing library met the required specifications. The main features of this library are briefly given and a comparison with a fixed-precision interval arithmetic, on a specific problem, is presented. It shows that the overhead due to the multiple precision is completely acceptable. Eventually, some applications based on MPFI are given: robotics, isolation of polynomial real roots (by an algorithm combining symbolic and numerical computations) and approximation of real roots with arbitrary accuracy.


65G30 Interval and finite arithmetic
65H05 Numerical computation of solutions to single equations
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