共查询到20条相似文献,搜索用时 15 毫秒
1.
V. K. Jain 《Proceedings Mathematical Sciences》2009,119(1):37-43
For a polynomial of degree n, we have obtained an upper bound involving coefficients of the polynomial, for moduli of its p zeros of smallest moduli, and then a refinement of the well-known Eneström-Kakeya theorem (under certain conditions). 相似文献
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Piotr Pawlowski 《Proceedings of the American Mathematical Society》1999,127(5):1493-1497
Let be a complex polynomial of degree having zeros in a disk . We deal with the problem of finding the smallest concentric disk containing zeros of . We obtain some estimates on the radius of this disk in general as well as in the special case, where zeros in are isolated from the other zeros of . We indicate an application to the root-finding algorithms.
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Piotr Pawlowski 《Transactions of the American Mathematical Society》1998,350(11):4461-4472
If is univariate polynomial with complex coefficients having all its zeros inside the closed unit disk, then the Gauss-Lucas theorem states that all zeros of lie in the same disk. We study the following question: what is the maximum distance from the arithmetic mean of all zeros of to a nearest zero of ? We obtain bounds for this distance depending on degree. We also show that this distance is equal to for polynomials of degree 3 and polynomials with real zeros.
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LetP(Z)=αn Zn + αn-1Zn-1 +…+α0 be a complex polynomial of degree n. There is a close connection between the coefficients and the zeros of P(z). In this paper we prove some sharp inequalities concerning the coeffi-cients of the polynomial P(z) with restricted zeros. We also establish a sufficient condition for the separation of zeros of P(z). 相似文献
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V. K. Jain 《分析论及其应用》1990,6(4):18-24
In this paper we have improved Cauchy's bound for zeros of a polynomialp(z)=z
n+a
n+1
z
n-1+a
n-2
z
n-2+......+a
1
z+a
0. Our result is best possible and sharpens some other results also. 相似文献
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Bing He 《中国科学 数学(英文版)》2023,66(5):957-976
We investigate a generalized homogeneous Hahn polynomial in some detail. This polynomial includes as special cases the homogeneous Hahn polynomial and the homogeneous Rogers-Szeg o polynomial.A generating function, which contains a known generating function as a special case, is given. We also give a finite series generating function. Some results on the asymptotic expansion for this polynomial are derived.Certain results on zeros are also obtained. We deduce several results on zeros of certain ... 相似文献
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In this paper, the properties of the generalized Euler-Frobenius polynomial Πn(·, q) are studied. It is proved that its zeroes are separated by the factor q and their asymptotic behavior, as q → ∞, is given. As a consequence, it is shown that least squares spline approximation on a biinfinite geometric mesh can be bounded independently of the (local) mesh ratio q and that the norm of the inverse of the corresponding order kB-spline Gram matrix decreases monotonically to 2k − 1 for large q, as q → ∞. 相似文献
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Àrpàd Elbert Andrea Laforgia 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(4):521-526
We investigate the behaviour with respect to the parameter > 0 of the zeros of the solutions of the differential equation y+y=0. We show that under appropriate restrictions such zeros are logconvex.Work sponsored by CNR, Gruppo Nazionale per l'Informatica Matematica, of Italy. 相似文献
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D. N. Zaporozhets 《Journal of Mathematical Sciences》2006,137(1):4525-4530
In this note, we find the distibution of the number of real zeros of a random polynomial. We also derive a formula for the
expected number of complex zeros lying in a given domain of the complex plane. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 69–79. 相似文献
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Summary A family of inclusion sets for the zeros of a complex polynomial is derived from the Lagrangean interpolation formulas. The optimization of the inclusion leads to a special type of matrix eigenvalue problem previously considered by several authors in connection with minimal Gershgorin discs. 相似文献
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Zbigniew Jelonek 《manuscripta mathematica》2003,110(2):145-157
Let be a polynomial dominant mapping and let deg f
i
≤d. We prove that the set K(f) of generalized critical values of f is contained in the algebraic hypersurface of degree at most D=(d+s(m−1)(d−1))
n
, where . This implies in particular that the set B(f) of bifurcations points of f is contained in the hypersurface of degree at most D=(d+s(m−1)(d−1))
n
. We give also an algorithm to compute the set K(f) effectively.
Received: 11 June 2001 / Revised version: 1 July 2002 Published online: 24 January 2003
The author is partially supported by the KBN grant 2 PO3A 017 22.
Mathematics Subject Classification (2000): 14D06, 14Q20, 51N10, 51N20, 15A04 相似文献
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We prove that for any zero α of the Alexander polynomial of a two-bridge knot, −3<Re(α)<6. Furthermore, for a large class of two-bridge knots we prove −1<Re(α). 相似文献
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The main purpose of this paper is to present a quicker and less memory-expensive algorithm for the generalized inversionof polynomial matrices than those presented earlier (Karampetakis,1997a Computation of the generalized inverse of a polynomialmatrix and applications. Linear Algebr. Appl. 252, 3560 and Karampetakis, 1997b Generalized inverses of two variable polynomial matrices and applications. Circuit Syst. & Signal Process. 16, 439453).
Received 24 January, 1999.
+ karampetakis@ccf.auth.gr 相似文献
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