An Algorithm to Represent Positive Semi-Definite Polynomials to Sum of Lader-Like Squares of Polynomials with Rational Coefficients
In this paper,the authors present a method to express a univariate posi-tive semi-definite polynomial into the sum of lader-like squares,i.e.,squares of several polynomials which degrees are strictly decreasing.When the coefficients of the given polynomial are rational numbers,the coefficients of the degree-descending polyno-mials are also rational numbers.The authors have also extended the method to multi-variate polynomials.Namely,if a multi-variate polynomial has any sum of square representation,then a special representation with rational coefficients of this polynomial can be obtained using this method.
Positive semi-definite polynomialsum of squares of polynomialssum of lader-like squaresrational SOS
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