• 호남수학학술지
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• 제42권2호
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• pp.269-291
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• 2020

In this paper, we get acquainted to a new generalization of the modified Hermite matrix polynomials. An explicit representation and expansion of the Matrix exponential in a series of these matrix polynomials is obtained. Some important properties of Modified Hermite Matrix polynomials such as generating functions, recurrence relations which allow us a mathematical operations. Also we drive expansion formulae and some operational representations.

• 호남수학학술지
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• 제41권1호
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• pp.35-49
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• 2019

In this work, it is shown that the combination of operational techniques and the use of the principle of quasi-monomiality can be a very useful tool for a more general insight into the theory of matrix polynomials and for their extension. We explore the formal properties of the operational rules to derive a number of properties of certain class of matrix polynomials and discuss the operational links with various known matrix polynomials.

• 대한수학회논문집
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• 제21권2호
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• 대한수학회논문집
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• 제37권1호
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• pp.303-326
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• 2022

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an 𝜔-dependent function f but also the values of its first derivative at three unequally spaced nodes. The function f is of the form, f(x) = g₁(x) cos(𝜔x) + g₂(x) sin(𝜔x), x ∈ [a, b], where g₁ and g₂ are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas I_N built on the foundation using N unequally spaced nodes. Then the coefficients of I_N are determined by solving a linear system, and some of the properties of these coefficients are obtained. When N is 2 or 3, some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with I_N. For N = 3, the errors for I_N are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

• 한국수자원학회논문집
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• 제32권3호
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• pp.237-246
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• 1999

자유수면 흐름의 모의를 위한 유한요소모형이 동수역학적 흐름방정식과 collocation 유한요소법에 의해 모의하였다. collocation 기법은 Hermite 다항식을 가진 접합점에서 적용이 되며, 메크릭스 방정식은 skyline 기법에 의해 해석하였다. 본 연구 모형은 마찰이 없는 수평수로에서의 정상도수, 비선형 표면전파 그리고 댐 파괴해석에 적용하였다. 계산결과 Bubnov-Galerkin 과 Petrov-Galerkin 기법과 비교하였다. 실제하천에 대한 적용성을 검토하기 위해서 북한강 유역에 적용하여 해석하였는데, 계산결과는 유량수문곡선에 있어서 기존의 DWOPER 모형의 결과와 일치하였다. Collocation 기법은 개수로 흐름에서의 점변 및 급변 부정류흐름을 모의하기 위해서 적절한 기법임을 확인할 수 있었다.