On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials

Thanh  Hieu  Le; Marc  Van  Barel

doi:10.3934/naco.2016001

Article Contents

2016, Volume 6, Issue 2: 91-102. Doi: 10.3934/naco.2016001

This issue Previous Article Next Article Index-proper nonnegative splittings of matrices

On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials

Thanh Hieu Le^1, and
Marc Van Barel^2,

1.
Department of Mathematics, Quy Nhon University
2.
Department of Computer Science, KU Leuven

Received: October 2014

Revised: March 2016

Published: May 2016

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Abstract

This paper presents a lower and upper bound of the Pythagoras number of sum of square magnitudes of Laurent polynomials (sosm-polynomials). To prove these bounds, properties of the corresponding system of quadratic polynomial equations are used. Applying this method, a new proof for the best (known until now) upper bound of the Pythagoras number of real polynomials is also presented.

Keywords:

Pythagoras number,
sum of squares,
sum of square magnitudes of Laurent polynomials.

Mathematics Subject Classification: Primary: 11E25, 12Y05; Secondary: 65H10.

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