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Mathematics of Computation

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Almost power sum systems

Authors: V. I. Korobov and A. N. Bugaevskaya
Journal: Math. Comp. 85 (2016), 717-736
MSC (2010): Primary 65H10, 65D32; Secondary 30E05, 49N05
Published electronically: June 26, 2015
MathSciNet review: 3434878
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Abstract: We consider the system of nonlinear almost polynomial equations without power gaps or with even power gaps. The method is to reduce the given system to finding the roots of univariate functions, some of which are polynomials. For the system with even power gaps the obtained equalities are the analogs of Newton's identities. These equalities express the connection between elementary symmetric functions and odd power sums.

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Additional Information

V. I. Korobov
Affiliation: V.N. Karazin Kharkov National University, 4 Svoboda sq., 61022 Kharkov, Ukraine
Address at time of publication: Institute of Mathematics, Szczecin University, Wielkopolska str. 15, 70–451 Szczecin, Poland

A. N. Bugaevskaya
Affiliation: Belgorod State University, 85 Pobeda str., 308015 Belgorod, Russia

Keywords: Systems of almost polynomial equations, moment problem, elementary symmetric functions, power sums, quadrature formulas
Received by editor(s): July 10, 2013
Received by editor(s) in revised form: February 4, 2014, July 11, 2014, and August 27, 2014
Published electronically: June 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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