• 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

• 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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.20 no.11
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• pp.1217-1224
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• 2009

This paper newly proposes a methodology towards computing antenna element weights which are satisfying asymmetric sidelobe levels(SLLs) specified arbitrarily on both sides of the main beam pattern, in the linear phased array antenna pattern synthesis problem. Opposite to the conventional methods in which the element weights are directly optimized from the array factor, this method is based on the optimum perturbations of complex roots inherent to the Schelkunoff's polynomial form which is described for the array factor. From the proposed methodology, the capability of nulling the directions of multiple jammers is also possible by independently perturbing only the complex roots corresponding to each jamming direction, hence allowing an enhancement of the simplicity of the numerical procedure by means of a proper reduction of the dimension of the solution space. The complex weights over the array are then easily computed by substituting the optimally perturbed complex roots to the Schelkunoff's polynomial. Some examples are examined and numerically verified by substituting the extracted weights into the array factor equation.