Bounds on polynomial roots using intercyclic companion matrices
نویسندگان
چکیده
منابع مشابه
Roots Multiplicity without Companion Matrices
We show a method for constructing a polynomial interpolating roots’ multiplicities of another polynomial, that does not use companion matrices. This leads to a modification to Guersenzvaig– Szechtman square-free decomposition algorithm that is more efficient both in theory and in practice. The problem of computing the square-free decomposition of a polynomial is well established in the realm of...
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Several matrix norms of the classical Frobenius companion matrices of a monic polynomial p(z) have been used in the literature to obtain simple lower and upper bounds on the absolute values of the roots λ of p(z). Recently, M. Fiedler has introduced a new family of companion matrices of p(z) (Lin. Alg. Appl., 372 (2003) 325-331) that has received considerable attention and it is natural to inve...
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In classical linear algebra, the eigenvalues of a matrix are sometimes defined as the roots of the characteristic polynomial. An algorithm to compute the roots of a polynomial by computing the eigenvalues of the corresponding companion matrix turns the tables on the usual definition. We derive a firstorder error analysis of this algorithm that sheds light on both the underlying geometry of the ...
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Computing roots of scalar polynomials as the eigenvalues of Frobenius companion matrices using backward stable eigenvalue algorithms is a classical approach. The introduction of new families of companion matrices allows for the use of other matrices in the root-finding problem. In this paper, we analyze the backward stability of polynomial root-finding algorithms via Fiedler companion matrices....
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2018
ISSN: 0024-3795
DOI: 10.1016/j.laa.2017.11.002