Pseudo-zero set

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 [math]\displaystyle{ \mathbb{C}^{m+1} }[/math] 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.

See also

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

References

• 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". International Conference on Computer Algebra in Scientific Computing. Springer. http://www.cargo.wlu.ca/casc2005/posters/StefGraillat.pdf.