Bounds on the Pythagoras number of the sum of square magnitudes of complex polynomials
نویسندگان
چکیده
This paper presents lower and upper bounds on the Pythagoras number of sum of square magnitudes of complex polynomials using well-known results on a system of quadratic polynomial equations. Applying this method, a new proof for the upper bound of the Pythagoras number of real polynomials is also presented.
منابع مشابه
The Pythagoras number of real sum of squares polynomials and sum of square magnitudes of polynomials
In this paper, we conjecture a formula for the value of the Pythagoras number for real multivariate sum of squares polynomials as a function of the (total or coordinate) degree and the number of variables. The conjecture is based on the comparison between the number of parameters and the number of conditions for a corresponding low-rank representation. This is then numerically verified for a nu...
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