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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the evaluation of some sparse polynomials
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by Dorian Nogneng and Éric Schost PDF
Math. Comp. 87 (2018), 893-904 Request permission


We give algorithms for the evaluation of sparse polynomials of the form \[ P=p_0 + p_1 x + p_2 x^4 + \cdots + p_{N-1} x^{(N-1)^2},\] for various choices of coefficients $p_i$. First, we take $p_i=p^i$, for some fixed $p$; in this case, we address the question of fast evaluation at a given point in the base ring, and we obtain a cost quasi-linear in $\sqrt {N}$. We present experimental results that show the good behavior of this algorithm in a floating-point context, for the computation of Jacobi theta functions.

Next, we consider the case of arbitrary coefficients; for this problem, we study the question of multiple evaluation: we show that one can evaluate such a polynomial at $N$ values in the base ring in subquadratic time.

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Additional Information
  • Dorian Nogneng
  • Affiliation: LIX, Bâtiment Alan Turing, Campus de l’École Polytechnique, 91120 Palaiseau, France
  • MR Author ID: 1122361
  • Email:
  • Éric Schost
  • Affiliation: David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • MR Author ID: 672551
  • Email:
  • Received by editor(s): February 16, 2016
  • Received by editor(s) in revised form: February 23, 2016, and September 16, 2016
  • Published electronically: September 7, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Math. Comp. 87 (2018), 893-904
  • MSC (2010): Primary 68W30; Secondary 11Y16
  • DOI:
  • MathSciNet review: 3739222