• 한국융합학회논문지
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• 제12권6호
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• pp.91-97
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• 2021

본 연구는 지역 인문학 생태계 조사와 지역 인문학 활용에 대한 조사를 하였다. 이를 통해 지역민들을 위한 인문학 생태계 활성화 방안에 대해 제시하였다. 연구내용으로 첫째, 지역 인문학 지원방안은 무엇인지 살펴보았다. 둘째, 지역 인문학 발전을 위한 연구인력 활용사업 방안을 찾고자 하였고 셋째, 지역 인문학 생태계 발전 연구인력 양성 방안을 연구하였다. 넷째, 지역 인문학 발전을 위한 일자리 창출 방안에 대한 내용을 분석하였다. 이러한 분석은 지역만의 고유한 문화와 특수함이 부여된 지역 인문학 생태계 연구 활성화를 위한 지원방안을 확립하는 데 있다.

• 대한수학회보
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• 제61권2호
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• pp.479-488
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• 2024

Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is C¹-smooth on [0, ∞), vanishes at zero, and is positive on (0, ∞). A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.

• 대한수학회지
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• 제53권4호
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• pp.781-793
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• 2016

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

• East Asian mathematical journal
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• 제24권1호
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• pp.21-25
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• 2008

The semilocal convergence of the secant method under $H{\ddot{o}}lder$ continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and finer error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh refinement strategies and to solve equations involving autonomous differential equations [1], [4], [7], [8].

• 대한수학회지
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• 제51권6호
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• pp.1155-1175
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• 2014

We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost our semilocal convergence criteria can be weaker; the error bounds more precise and in the local case the convergence balls can be larger and the error bounds tighter than in earlier studies such as [1-3,7-14,16,20,21] at least for the cases of Newton's method and the secant method. Numerical examples are also presented to illustrate the theoretical results obtained in this study.

• 충청수학회지
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• 제25권2호
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• pp.267-275
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• 2012

We present new results for the local convergence of Newton's method to a unique solution of an equation in a Banach space setting. Under a flexible gamma-type condition [12], [13], we extend the applicability of Newton's method by enlarging the radius and decreasing the ratio of convergence. The results can compare favorably to other ones using Newton-Kantorovich and Lipschitz conditions [3]-[7], [9]-[13]. Numerical examples are also provided.

• East Asian mathematical journal
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• 제26권3호
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• pp.365-370
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• 2010

A local convergence result is provided for the continuous analog of Newton's method in a Banach space setting. The radius of convergence is larger, the error bounds tighter, and under the same or weaker hypotheses than before [12].

• East Asian mathematical journal
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• 제23권2호
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• pp.261-270
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• 2007

We provide a local convergence analysis for Secant-like algorithm for solving nonsmooth variational inclusions in Banach spaces. An existence-convergence theorem and an improvement of the ratio of convergence of this algorithm are given under center-conditioned divided difference and Aubin's continuity concept. Our result compare favorably with related obtained in [16].

• 대한수학회논문집
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• 제33권2호
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• 대한수학회지
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• 제51권5호
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• pp.955-970
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• 2014

We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.