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In complex analysis (a branch of mathematical 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 those of p by a small amount. Namely, given a norm |·| on the space ${\displaystyle \mathbb {C} ^{m+1}}$ of polynomial coefficients, the pseudo-zero set is the set of all zeros of all degree-m polynomials q such that |p − q| (as vectors of coefficients) is less than a given ε.

• List of complex analysis topics
• Timeline of calculus and mathematical analysis

• 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. S2CID  22850276.
• 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). International Conference on Computer Algebra in Scientific Computing. Springer.

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