NDLI: The nearest polynomial with a zero in a given domain from a geometrical viewpoint

Content Provider	ACM Digital Library
Author	Sekigawa, Hiroshi
Abstract	For a real univariate polynomial f and a closed complex domain D, whose boundary C is a simple curve parameterized by a univariate piecewise rational function, a rigorous method is given for finding a real univariate polynomial f such that f has a zero in D and \|f - $~f\|_{∞}$ is minimal. First, it is proved that the minimum distance between f and polynomials having a zero at α in C is a piecewise rational function of the real and imaginary parts of α. Thus, on C, the minimum distance is a piecewise rational function of a parameter obtained through the parameterization of C. Therefore, by using the property that ~f has a zero on C and computing the minimum distance on C, ~f can be constructed.
Starting Page	287
Ending Page	294
Page Count	8
File Format	PDF
ISBN	9781595939043
DOI	10.1145/1390768.1390808
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-07-20
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Polynomial L^∞-norm Zero Perturbation Davenport-schinzel sequence
Content Type	Text
Resource Type	Article

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The nearest polynomial with a zero in a given domain from a geometrical viewpoint