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 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.
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" (PDF). Computer Algebra in Scientific Computing: 8th International Workshop, CASC 2005, Kalamata, Greece, September 12–16, 2005, Proceedings (Lecture Notes in Computer Science). http://www.cargo.wlu.ca/casc2005 . Springer.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
