The numerical radius and bounds for zeros of a polynomial
نویسندگان
چکیده
منابع مشابه
On Numerical Radius of a Matrix and Estimation of Bounds for Zeros of a Polynomial
We obtain inequalities involving numerical radius of a matrix A ∈ M n C. Using this result, we find upper bounds for zeros of a given polynomial. We also give a method to estimate the spectral radius of a given matrix A ∈ M n C up to the desired degree of accuracy.
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An algorithm for the computation of error bounds for the zeros of a polynomial is described. This algorithm is derived by applying Rouch6's theorem to a Newton-like interpolation formula for the polynomial, and so it is suitable in the case where the approximations to the zeros of the polynomial are computed successively using deflation. Confluent and clustered approximations are handled easily...
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In this paper we find new estimate for the numerical radius of a given matrix, and we prove that, this estimate is better than any estimate for the numerical radius. We present also new bounds for the zero of polynomials by using new estimate for the numerical radius of a companion matrix of a given polynomial and matrix inequalities.
متن کاملInequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin
Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$, let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$. Dewan et al proved that if $p(z)$ has all its zeros in $|z| leq k, (kleq 1),$ with $s$-fold zeros at the origin then for every $alphainmathbb{C}$ with $|alpha|geq k$, begin{align*} max_{|z|=...
متن کاملOn Bounds For The Zeros of Univariate Polynomial
Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06623-6