Scaled generalized Bernstein polynomials and containment regions for the zeros of polynomials

Authors:
Hansjörg Linden
Affiliations:
Fachbereich Mathematik der FernUniversität, Postfach 940, Lützowstr. 125, 58084 Hagen, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

Let P"n(x)=@?"k"="0^n@b"kb"k","n(x;@a,@b),@b"n0, where b"k","n(x;@a,@b)@?(@a+x)^k(@b-x)^n^-^k,k=0,1,...,n,@a,@b@?C,@a-@b, a generalized scaled Bernstein polynomial. Extending a result of Winkler [A resultant matrix for scaled Bernstein polynomials, Linear Algebra Appl. 319 (2000) 179-191] a companion matrix for P"n is given. The application of some matrix methods to this companion matrix yields regions for the zeros of P"n.