Pseudo-zero set

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In complex analysis, the pseudo-zero set or root neighborhood of a degree-m polynomial p(z) is the set of all complex numbers that are roots of polynomials whose coefficients differ from p's by a small amount. Namely, given a norm |·| on \mathbb{C}^{m+1}, the pseudo-zero set is the set of all zeros of degree-m polynomials q such that |p-q| (as vectors) is less than a given ε.


  • Farouki, Rida T; Chang Yong Han (12 January 2007). "Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems". Applicable Algebra in Engineering, Communication and Computing 18 (1-2): 169–189. doi:10.1007/s00200-006-0027-4. 
  • Graillat, Stef (2005). "Pseudozero Set of Multivariate Polynomials" (PDF). Computer Algebra in Scientific Computing: 8th International Workshop, CASC 2005, Kalamata, Greece, September 12–16, 2005, Proceedings (Lecture Notes in Computer Science). |conferenceurl= missing title (help). Springer.