半代数集中有根多项式的表征

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) Pub Date : 2003-12-09 DOI:10.1109/CDC.2003.1271686

J. Lasserre

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引用次数: 3

摘要

设p /spl epsi/ R[x]为实值多项式，S /spl下标/ C为C[z, z~]中某些多项式g/下标k/的多项式不等式gk(z, z~)/spl ges/0所定义的半代数集。我们给出了p的系数的一个充分必要条件，使p的所有零点都在S内。

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Characterizing polynomials with roots in a semi-algebraic set

Let p /spl epsi/ R[x] be a real-valued polynomial and S /spl sub/ C a semi-algebraic set defined by polynomial inequalities gk(z, z~)/spl ges/0 for some polynomials g/sub k/ in C[z, z~]. We provide a necessary and sufficient condition on the coefficients of p for all the zeros of p to be in S.

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42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)

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