Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

Request Permissions   Purchase Content 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65H10, 65D32, 30E05, 49N05

Retrieve articles in all journals with MSC (2010): 65H10, 65D32, 30E05, 49N05


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
Email: korobow@univ.szczecin.pl

A. N. Bugaevskaya
Affiliation: Belgorod State University, 85 Pobeda str., 308015 Belgorod, Russia
Email: bugaevskaya@bsu.edu.ru

DOI: https://doi.org/10.1090/mcom/2994
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