On Decompositions of Real Polynomials Using Mathematical Programming Methods

• 作者: Janez Povh
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: COMMUTATIVE POLYNOMIAL NONCOMMUTATIVE POLYNOMIAL Sum Of Squares SEMIDEFINITE Programming Newton POLYTOPE
• 年，卷（期）: 2011,（3）
• 页码范围: 309-314
• 页数: 6页
• 分类号: O1

摘要

We present a procedure that gives us an SOS (sum of squares) decomposition of a given real polynomial in variables, if there exists such decomposition. For the case of real polynomials in non-commutative variables we extend this procedure to obtain a sum of hermitian squares SOHS) decomposition whenever there exists any. This extended procedure is the main scientific contribution of the paper.