Fast online multiplication of real numbers

  • Matthias Schröder
Algorithms II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)


We develop an online-algorithm for multiplication of real numbers which runs in time O(M(n)log(n)), where M denotes the Schönhage-Strassen-bound for integer multiplication which is defined by M(m)=m log(m) log log(m), and n refers to the output precision (1/2)n. Our computational model is based on Type-2-machines: The real numbers are given by infinite sequences of symbols which approximate the reals with increasing precision. While reading more and more digits of the input reals, an algorithm for a real function produces more and more precise approximations of the desired result. An algorithm M is called online, if for every n ∈ ℕ the input-precision, which M requires for producing the result with precision (1/2)n, is approximately the same as the topologically necessary precision.


Computable real analysis computational complexity online computations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Matthias Schröder
    • 1
  1. 1.Theoretische Informatik IFernUniversität HagenHagenGermany

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