منابع مشابه
Perturbing polynomials with all their roots on the unit circle
Given a monic real polynomial with all its roots on the unit circle, we ask to what extent one can perturb its middle coefficient and still have a polynomial with all its roots on the unit circle. We show that the set of possible perturbations forms a closed interval of length at most 4, with 4 achieved only for polynomials of the form x2n + cxn + 1 with c in [−2, 2]. The problem can also be fo...
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We study the geometry, topology and Lebesgue measure of the set of monic conjugate reciprocal polynomials of fixed degree with all roots on the unit circle. The set of such polynomials of degree N is naturally associated to a subset of R. We calculate the volume of this set, prove the set is homeomorphic to the N − 1 ball and that its isometry group is isomorphic to the dihedral group of order ...
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In our last lecture, we studied two root-finding methods that each took in a polynomial f(x) and an interval [a, b], and returned a root of that function on that interval. This was great for the problem we asked at the start of the class — how to find a root of a quintic polynomial — but is not necessarily so great for many other problems we may want to study. For example, we may want to find a...
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ژورنال
عنوان ژورنال: Lithuanian Mathematical Journal
سال: 2009
ISSN: 0363-1672,1573-8825
DOI: 10.1007/s10986-009-9052-x