半正定多项式的构造与逐次差分代换的加速

Construction of Semi-Definite Polynomials and Acceleration of Successive Differential Substitution

给出了若干构造半正定多项式的类型和方法,列举了大量问题和例子,并给出了部分解答;提出了解决扩展级递增不等式猜想的一个思路,把多项式f分成正部p(f)和负部n(f)两部分,并用p(f)和n(f)构造了若干逐次差分代换sds的加速因子,从而解决了一大类多项式的正性判定问题.

Several approaches for the construction of semi-definite polynomials are given and examples and solutions are shown. The polynomial f is divided into positive part p（f） and negative part n（f）. The polynomials p（f） and n（f） is used to construct the acceleration factor in successive differential substitution to solve a class of semidclinile problems.