Pseudo-zero set

Pseudo-zero set

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 "ps 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".

References

*cite journal|last=Farouki|first=Rida T|coauthors=Chang Yong Han|year=2007|month=January|day=12|title=Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems|journal=Applicable Algebra in Engineering, Communication and Computing|volume=18|issue=1-2|pages=169–189|doi=10.1007/s00200-006-0027-4
*cite conference|last=Graillat|first=Stef|title=Pseudozero Set of Multivariate Polynomials|year=2005|conferenceurl=http://www.cargo.wlu.ca/casc2005/|url=http://www.cargo.wlu.ca/casc2005/posters/StefGraillat.pdf|format=PDF|booktitle=Computer Algebra in Scientific Computing: 8th International Workshop, CASC 2005, Kalamata, Greece, September 12-16, 2005, Proceedings (Lecture Notes in Computer Science)|publisher=Springer


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