A Facility Location Formulation for Stable Polynomials and Elliptic Fekete Points

作者：Beltran Carlos^*

来源：Foundations of Computational Mathematics, 2015, 15(1): 125-157.

DOI：10.1007/s10208-014-9213-0

• Elliptic Fekete points
• Stable polynomials
• Logarithmic energy
• Smale's 7th problem
• Facility location
• Cap discrepancy

A breakthrough paper written in 1993 by Shub and Smale unveiled the relationship between stable polynomials and points which minimize the discrete logarithmic energy on the Riemann sphere (a.k.a. elliptic Fekete points). This relationship has inspired advances in the study of both concepts, many of whose main properties are not well known yet. In this paper I prove an equivalent formulation for the problem of elliptic Fekete points and some consequences, including a (nonsharp) reciprocal of Shub and Smale's result and some novel nontrivial claims about these classical problems.

• 出版日期2015-2