• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.351-360
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• 2006

In this paper, we develop an inexact-Newton method for solving nonsmooth operator equations in infinite-dimensional spaces. The linear convergence and superlinear convergence of inexact-Newton method under some conditions are shown. Then, we characterize the order of convergence in terms of the rate of convergence of the relative residuals. The present inexact-Newton method could be viewed as the extensions of previous ones with same convergent results in finite-dimensional spaces.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.455-464
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• 2014

We establish some new criteria for the oscillation of mth order nonlinear difference equations. We study the case of strongly superlinear and the case of strongly sublinear equations subject to various conditions. We also present a sufficient condition for every solution to be asymptotic at ${\infty}$ to a factorial expression $(t)^{(m-1)}$.

• 대한수학회지
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• 제34권1호
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• pp.247-255
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• 1997

In this paper, we are concerned with the existence of positive solutions for the boundary value problems of the form; $$(1) u"(t) + q(t)g(u(t)) = 0, 0 < t < 1 $$ $$ u(0) = 0 = u(1), $$ where q is singular at 0 and /or 1.or 1.

• 대한수학회논문집
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• 제4권1호
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• pp.47-57
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• 1989

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.721-736
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• 2014

We consider the equation ${\Delta}_mu=p(x)u^{\alpha}+q(x)u^{\beta}$ on $R^N(N{\geq}2)$, where p, q are nonnegative continuous functions and 0 < ${\alpha}{\leq}{\beta}$. Under several hypotheses on p(x) and q(x), we obtain existence and nonexistence of blow-up solutions both for the superlinear and sublinear cases. Existence and nonexistence of entire bounded solutions are established as well.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.345-360
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• 2001

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the mth(m≥2 an integer). Radius of convergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover, we show that under hypotheses on the mth Frechet-derivative our radius of convergence can sometimes be larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger than the one in [10].

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.193-208
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• 2006

A modified BFGS algorithm for solving the unconstrained optimization, whose Hessian matrix at the minimum point of the convex function is of rank defects, is presented in this paper. The main idea of the algorithm is first to add a modified term to the convex function for obtain an equivalent model, then simply the model to get the modified BFGS algorithm. The superlinear convergence property of the algorithm is proved in this paper. To compared with the Tensor algorithms presented by R. B. Schnabel (seing [4],[5]), this method is more efficient for solving singular unconstrained optimization in computing amount and complication.

• 대한수학회보
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• 제43권4호
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• pp.693-701
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• 2006

Using Minimax principle and Linking theorem in critical point theory, we prove the existence of two nontrivial solutions for the following second order superlinear difference systems $$(P)\{{\Delta}^2x(k-1)+g(k,y(k))=0,\;k{\in}[1,\;T],\;{\Delta}^2y(k-1)+f(k,\;x(k)=0,\;k{\in}[1,\;T],\;x(0)=y(0)=0,\;x(T+1)=y(T+1)=0$$ where T is a positive integer, [1, T] is the discrete interval {1, 2,..., T}, ${\Delat}x(k)=x(k+1)-x(k)$ is the forward difference operator and ${\Delta}^2x(k)={\Delta}({\Delta}x(k))$.

• 디지털콘텐츠학회 논문지
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• 제10권4호
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• pp.579-585
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• 2009

Tyrtshnikov[9]의 연구에서는 토플리츠 선형시스템에서 토플리츠 선행조건으로 일반해를 구하는 방법들을 제시하고 있다. 또한 대칭 토플리츠 행렬에서의 선행조건 행렬을 선택하는 방법도 소개 하였다. 본 연구는 토플리츠 시스템에서 새롭게 선행조건 찾는 방법을 소개하고 있으며, 선행조건행렬들의 분석을 통해 대칭 토플리츠 행렬의 고유값들과 대칭 토플리츠행렬로 부터 생성된 선행조건행렬의 고유값들이 매우 근접하다는 결과를 나타내고 있다. 즉, 선행조건시스템 $C_0^{-1}T$의 고유값들은 1에 모두 접근하게되면, 선행조건 시스템의 수렴속도는 superlinear이다. 본 연구에서 생성된 선행조건행렬 $C_0$은 선행조건시스템의 superlinear의 수렴속도로 계산하게 된다. 또한 토플리츠 행렬은 이미지 프로세싱이나 시그널 프로세싱에서 많이 응용되고 있으므로 본 연구에서 개발한 선행조건행렬로부터 다양한 응용성을 높일 수 있다. 본연구의 또 다른 특징은 토플리츠 행렬의 중요한 성질을 보존하면서 선행조건행렬을 생성하였다.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.569-578
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• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.