Fast Multiprecision Evaluation of Series of Rational Numbers
نویسندگان
چکیده
We describe two techniques for fast multiple-precision evaluation of linearly convergent series, including power series and Ramanujan series. The computation time for N bits is O((logN)M(N)), whereM(N) is the time needed to multiply twoN -bit numbers. Applications include fast algorithms for elementary functions, π, hypergeometric functions at rational points, ζ(3), Euler’s, Catalan’s and Apéry’s constant. The algorithms are suitable for parallel computation.
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تاریخ انتشار 1998