# American Institute of Mathematical Sciences

2016, 6(2): 91-102. doi: 10.3934/naco.2016001

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

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

Received  October 2014 Revised  March 2016 Published  June 2016

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.
Citation: Thanh Hieu Le, Marc Van Barel. On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 91-102. doi: 10.3934/naco.2016001
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