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Erschienen in:
2007 | OriginalPaper | Buchkapitel
On the Location of Zeros of an Interval Polynomial
verfasst von : Hiroshi Sekigawa, Kiyoshi Shirayanagi
Erschienen in: Symbolic-Numeric Computation
Verlag: Birkhäuser Basel
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For an interval polynomial
F
, we provide a rigorous method for deciding whether there exists a polynomial in F that has a zero in a prescribed domain
D
. When
D
is real, we show that it is sufficient to examine a finite number of polynomials. When
D
is complex, we assume that the boundary
C
of
D
is a simple closed curve of finite length and
C
is represented by a piecewise rational function. The decision method uses the representation of
C
and the property that a polynomial in
F
is of degree one with respect to each coefficient regarded as a variable. Using the method, we can completely determine the set of real numbers that are zeros of a polynomial in
F
. For complex zeros, we can obtain a set
X
that contains the set
Z
(
F
), which consists of all the complex numbers that are zeros of a polynomial in
F
, and the difference between
X
and
Z
(
F
) can be as small as possible.