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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 solving composite power polynomial equations
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by Yingquan Wu and Christoforos N. Hadjicostis PDF
Math. Comp. 74 (2005), 853-868 Request permission

Abstract:

It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton’s identities. In this work, by further exploring Newton’s identities, we discover a binomial decomposition rule for composite elementary symmetric polynomials. Utilizing this decomposition rule, we solve three types of systems of composite power polynomial equations by converting each type to single-variable polynomial equations that can be solved easily. For each type of system, we discuss potential applications and characterize the number of nontrivial solutions (up to permutations) and the complexity of our proposed algorithmic solution.
References
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Additional Information
  • Yingquan Wu
  • Affiliation: Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Illinois 61801
  • Address at time of publication: 139 Coordinated Science Laboratory, 1308 West Main Street, Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Illinois 61801-2307
  • Email: ywu4@uiuc.edu
  • Christoforos N. Hadjicostis
  • Affiliation: Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Illinois 61801
  • Address at time of publication: 357 Coordinated Science Laboratory, 1308 West Main Street, Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Illinois 61801-2307
  • Email: chadjic@uiuc.edu
  • Received by editor(s): October 9, 2002
  • Received by editor(s) in revised form: September 5, 2003
  • Published electronically: August 20, 2004
  • Additional Notes: This material is based upon work supported in part by the National Science Foundation under NSF Career Award 0092696 and NSF ITR Award 0085917 and in part by the Motorola Research Center at the University of Illinois. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the NSF or Motorola.
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 853-868
  • MSC (2000): Primary 65H10; Secondary 12Y05
  • DOI: https://doi.org/10.1090/S0025-5718-04-01710-7
  • MathSciNet review: 2114652