• Journal of the Korean Data and Information Science Society
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• v.16 no.1
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• pp.127-136
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• 2005

We will derive some results on the perturbation of roots using Newton's interpolation formula. And we also compare our results with those obtained by Ostrowski by giving some numerical experiments with Wilkinson's polynomials.

• The Pure and Applied Mathematics
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• v.10 no.1
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• pp.37-47
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• 2003

We will show that any linear perturbation of polynomials that introduces bounded perturbations into the roots of polynomial is some linear combination of the derivatives of a polynomial. And we will derive an absolute root bound functional which is in some sense better than the other known absolute root bound functionals.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.61-76
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• 1995

Much research has been done to estimate the magnitudes of the changes of the roots from the perturbed polynomials. For more information and references on such work, see [2, 4, 5, 10, 17].

• Kyungpook Mathematical Journal
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• v.34 no.2
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• pp.207-216
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• 1994

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.5-9
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• 1995

In many cases of robust stability problems, the characteristic polynomial has real coefficients which or nonlinear functions of uncertain parameters. For this set of polynomials, a new stability easily checking algorithm for reducing the conservatism of the stability bound are given. It is the new stability theorem to determine the stability region just in parameter space. Illustrative example show that the presented method has larger stability bound in uncertain parameter space than others.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.77-85
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• 1997

In this work we will show that, in the sense of the Maximum overestimation factor, the absolute root bound functional derived from the new formula for the divided difference is better than the other known results in this area.

• Journal of Industrial Technology
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• v.11
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• pp.27-31
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• 1991

Consider a problem to keep half of the poles unchanged when some of the coefficients of stable characteristic polynomials are perturbed. A procedure was proposed for the problem. However, the pole assignment procedure has not been addressed. A simple algorithm for the procedure is proposed in this paper.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10a
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• pp.429-434
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• 1990

Given the polynomial in z, P$_{0}$ (z) = z$^{n}$ + a$_{1}$z$^{n-1}$ + a$_{2}$z$^{n-2}$ + ... + a$_{n-1}$z + a$_{0}$ , it is of interest to know how much coefficient a$_{I}$ can be perturbed while simultaneously preserving the stable property of the polynomials. In this paper, we derive the maximal intervals, centered about the nominal values of the coefficients, having the following property: the polynomial remains stable for all variations within these intervals. And then, under the unfixed weighted perturbation evaluate upper and lower allowable perturbations.tions.s.