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Zeros of Transformed Polynomials
SIAM Journal on Mathematical Analysis, 1990Transformations that map polynomials with zeros in a certain interval into polynomials with zeros in another interval are considered here. By using the theory of bi-orthogonal polynomials, a general technique for the construction of such transformations is developed. Finally, a list of 16 different transformations formed by using the authors’ technique
A. Iserles, S. P. Nørsett
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Zeros of Orthogonal Polynomials
2001Recall that given a weight W 2 on the finite or infinite interval I = (c, d), its nth orthonormal polynomial p n (W 2,x) has zeros \( \left\{ {{x_{{jn}}}} \right\}\begin{array}{*{20}{c}} n \hfill \\ {j = 1} \hfill \\ \end{array} , \), where $$ c < {x_{{nn}}} < {x_{{n - 1,n}}} < \cdot \cdot \cdot < {x_{{2n}}}{ < _{{1n}}} < d. "$$
Eli Levin, Doron S. Lubinsky
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Zero Distribution of Polynomials
2002The classical theorems of Jentzsch and Szego concern the limiting behavior of the zeros of the partial sums of a power series. More precisely, if are the partial sums of a power series having finite positive radius of convergence ρ, then Jentzsch [91] proved that each point of the circle of convergence C ρ := {z: |z| = ρ} is a limit point of ...
Vladimir V. Andrievskii +1 more
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Inequalities for Polynomial Zeros
2000This survey paper is devoted to inequalities for zeros of algebraic polynomials. We consider the various bounds for the moduli of the zeros, some related inequalities, as well as the location of the zeros of a polynomial, with a special emphasis on the zeros in a strip in the complex plane.
Gradimir V. Milovanović +1 more
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1993
We consider the complex polynomial p: C → C defined by $$p(z)=\sum\limits_{i=0}^n{{p_i}{z^i}},{p_i}\in\mathbb{C}{\text{, }}i=0, . . . , n, {p_n}\ne 0.$$ (1) (9.1) The Fundamental Theorem of algebra asserts that this polynomial has n zeros counted by multiplicity. Finding these roots is a non trivial problem in numerical mathematics.
Ulrich Kulisch +3 more
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We consider the complex polynomial p: C → C defined by $$p(z)=\sum\limits_{i=0}^n{{p_i}{z^i}},{p_i}\in\mathbb{C}{\text{, }}i=0, . . . , n, {p_n}\ne 0.$$ (1) (9.1) The Fundamental Theorem of algebra asserts that this polynomial has n zeros counted by multiplicity. Finding these roots is a non trivial problem in numerical mathematics.
Ulrich Kulisch +3 more
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Polynomials Whose Zeros Are Powers of a Given Polynomial’s Zeros
The American Mathematical Monthly, 2022openaire +1 more source
Polynomial arithmetic and zeros
2001We start by collecting some concepts, operations, and properties on multivariate polynomials, which are fundamental and will be used throughout the following chapters. Most of the results presented here are not proved formally; their proofs may be found in standard textbooks on algebra.
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