• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.747-760
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• 2014

In this paper a higher order iterative algorithm is developed for an unconstrained multivariate optimization problem. Taylor expansion of matrix valued function is used to prove the cubic order convergence of the proposed algorithm. The methodology is supported with numerical and graphical illustration.

• East Asian mathematical journal
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• 제33권5호
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• pp.511-525
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• 2017

We introduce an extrapolated higher order characteristic finite element method to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergence in both the temporal direction and the spatial direction in $L^2$ normed space is established and some computational results to support our theoretical results are presented.

• 충청수학회지
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• 제25권2호
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• pp.359-365
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• 2012

The purpose of this paper is to provide some corrections regarding algebraic flaws encountered in the paper entitled "Sixteenth-order method for nonlinear equations" which was published in January of 2010 by Li et al.[9]. Further detailed comments on their error equation are stated together with convergence analysis as well as high-precision numerical experiments.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.527-538
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• 2000

We provide sufficient conditions for the monotone convergence of a Chebysheff-Halley-type method or method of tangent hyperbolas in a partially ordered topological space setting. The famous kantorovich theorem on fixed points is used here.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.773-781
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• 2010

Recently, Yun [8] proposed a new three-step iterative method with the fourth-order convergence for solving nonlinear equations. By using his ideas, we develop a general form of multi-step iterative methods with higher order convergence for solving nonlinear equations, and then we study convergence analysis of the multi-step iterative methods. Lastly, some numerical experiments are given to illustrate the performance of the multi-step iterative methods.

• 충청수학회지
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• 제21권4호
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• pp.483-492
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• 2008

The k-fold pseudo-Newton's method is proposed and its convergence behavior is investigated near a simple zero. The order of convergence is proven to be at least k + 2. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. High-precison numerical results are successfully implemented via Mathematica and illustrated for various examples.

• 한국음향학회지
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• 제13권4호
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• pp.77-85
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• 1994

본 연구에서는 필터의 차수가 적절한 수준으로 자동적으로 조정되는, 최적 수렴 인자를 갖는 최대 경사 (steepest descent) 방식의 적응 알고리듬을 제안한다. 지금까지 적응 신호 처리의 여러 응용 분야에 적응 필터를 사용할 때, 사전 지식이나 경험에 비추어 필터 차수를 고정하여 이용하여 왔다. 하지만 실제 실행시 필요한 필터 차수를 알기는 어렵고 되도록 큰 차수의 필터를 실행해야만 한다. 이로 인하여 필터 차수가 너무 큰 경우 필요없는 계산량이 증가하게 된다. 제안한 가변 길이 최적 수렴 인자 알고리듬은 주어진 차수 한도 내에서 자동적으로 적절한 절터 차수를 찾아 동작하므로, 불필요한 계산량의 증가를 줄여서 결과적으로 수렴 속도의 향상과 정상 상태에서의 수렴 오차를 줄일 수 있다. 제안한 알고리듬의 타당성은 시스템 식별에 대한 컴퓨터 모의 실험으로 입증하였다.

• 충청수학회지
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• 제37권1호
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• 한국음향학회지
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• 제12권1호
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• pp.37-46
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• 1993

The adaptive algorithm for the Volterra filter is considered. Owing to its simplicity, the LMS algorithm for adaptive Volterra filter(AVF) is widely used as in linear adaptive filters. However, the convergence speed is unsatisfactory. For improving the convergence speed, the frequency domain LMS second order adaptive Volterra filter(FLMS-AVF) is proposed and analyzed. We show that the time and frequency domain LMS AVF's have the same steady state performance under approprate conditons. Moreover, it can be shown that this algorithm can improve the convergence speed significantly by applying self-orthogonalizing method.

• 충청수학회지
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• 제27권4호
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• pp.753-762
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• 2014

A three-step sextic simple-root finder is constructed with the use of weighting functions of derivative-to-derivative ratios. Their convergence and computational properties are investigated along with concrete numerical examples to verify the theoretical analysis.