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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.


A solution to certain polynomial equations with applications to nonlinear fitting
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by Chris Connell PDF
Math. Comp. 74 (2005), 303-319 Request permission


We present a combinatorial method for solving a certain system of polynomial equations of Vandermonde type in $2N$ variables by reducing it to the problem of solving two special linear systems of size $N$ and rooting a single univariate polynomial of degree $N$. Over $\mathbb {C}$, all solutions can be found with fixed precision using, up to polylogarithmic factors, $O(N^2)$ bitwise operations in the worst case. Furthermore, if the data is well conditioned, then this can be reduced to $O(N)$ bit operations, up to polylogarithmic factors. As an application, we show how this can be used to fit data to a complex exponential sum with $N$ terms in the same, nearly optimal, time.
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Additional Information
  • Chris Connell
  • Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
  • Address at time of publication: Department of Mathematics, Rawles Hall, Indiana University, Bloomington, Indiana 47401
  • MR Author ID: 666258
  • Email:
  • Received by editor(s): January 18, 2002
  • Received by editor(s) in revised form: January 6, 2003
  • Published electronically: July 9, 2004
  • Additional Notes: The author was supported in part by an NSF postdoctoral fellowship
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 303-319
  • MSC (2000): Primary 65H10
  • DOI:
  • MathSciNet review: 2085413