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We study ellipsoid bounds for the solutions
of polynomial systems of equalities and inequalities. The variable μ can be considered as parameters perturbing the solution
x. For example, bounding the zeros of a system of polynomials whose coefficients depend on parameters is a special case of
this problem. Our goal is to find minimum ellipsoid bounds just for x. Using theorems from real algebraic geometry, the ellipsoid
bound can be found by solving a particular polynomial optimization problem with sums of squares (SOS) techniques. Some numerical
examples are also given. 相似文献