• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.279-284
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• 2008

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n=4, 5, we find the constrained Jacobi polynomial, and for $n{\geq}6$, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

• Journal of Integrative Natural Science
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• v.9 no.2
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• pp.152-154
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• 2016

Arbitrary polynomial of degree n can be written in Chebyshev form. In this paper, we generalize this Chebyshev form and study its root distributions.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.172-181
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• 1999

Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.103-112
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• 1998

In this paper insertion of numerous control points to be performed by using the Chebyshev polynomial root at the selection of knot vector. This method introduces a simple method of knot refinement and it is applied in a developed program. The Chebyshev roots exist densely in broth ends of the range and are proposed more effective knot refinement to modify a surface. Therefore, generated control points are relatively uniform in specified knot interval. In the surface generation, a local insertion of numerous control points are easily inserted by using the characteristic of Chebyshev polynomial roots at knot refinement. It is possible to create a complex surface with a single surface. The number of control point can be reduced by using the local insertion of control points in a required shape

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.153-161
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• 2001

In the course of working on the preconditioning $C^1$ polynomial spline collocation method, one has to deal with the exponential decay of $C^1$ Lagrange polynomial splines. In this paper we show the exponential decay of $C^1$ Lagrange polynomial splines using the Chebyshev-Gauss points as the local data points.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.223-236
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• 2000

In this paper, we solve the Fredholm integral equation of the first and second kind when the kernel takes a singular form. Also, some important relations for Chebyshev polynomial of integration are established.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.429-437
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• 2019

Dilcher and Stolarsky [1] recently studied a sequence resembling the Chebyshev polynomials of the first kind. In this paper, we follow their some research directions to the Chebyshev polynomials of the second kind. More specifically, we consider a sequence resembling the Chebyshev polynomials of the second kind in two different ways, and investigate its properties including relations between this sequence and the sequence studied in [1], zero distribution and the irreducibility.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.677-682
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• 2007

The unique positive zero of $F_m(z):=z^{2m}-z^{m+1}-z^{m-1}-1$ leads to analogues of $2(\array{2n\\k}\)$(k even) by using hypergeometric functions. The minimal polynomials of these analogues are related to Chebyshev polynomials, and the minimal polynomial of an analogue of $2(\array{2n\\k}\)$(k even>2) can be computed by using an analogue of $2(\array{2n\\k}\)$. In this paper we show that the analogue of $2(\array{2n\\2}\)$. In this paper we show that the analygue $2(\array{2n\\2}\)$ is the only real zero of its minimal polynomial, and has a different representation, by using a polynomial of smaller degree than $F_m$(z).

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.261-275
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• 2002

Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.503-511
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• 2021

In this present work, we obtain certain coefficients of the subclass 𝓗_λ,𝛄(s, b, n) of non-Bazilević functions and estimate the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to this class.