• 대한수학회지
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• 제55권4호
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• Journal of the Korean Data and Information Science Society
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• 제27권4호
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• pp.993-1000
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• 2016

반응 값이 없는 자료를 지도학습 (supervised learning)에 사용하는 준지도 학습 (semi-supervised learning)은 분류에 더 많은 관심을 갖는다. 본 연구는 준지도학습을 회귀분석에 적용하는 준지도 회귀함수 추정법을 제안한다. 제안된 방법은 기존의 방법과 형태는 같지만 반응 값이 있는 자료와 없는 자료의 주변분포를 다르게 가정하고, 서로 다른 평활계수를 사용하는 등 좀 더 일반화된 형태를 가진다. 제안된 추정법의 점근분포를 계산하고 점근평균제곱오차를 최소화하는 최적의 평활계수가 가지는 조건을 찾는다. 설명변수의 주변분포에 대한 추정이 잘 이루이지고, 반응 값이 있는 자료와 없는 자료의 크기에 대한 조건을 적절하게 통제할 수 있고, 그리고 평활계수가 적절하게 선택될 수 있다면 라벨없는 자료가 회귀분석에서도 도움을 줄 수 있음을 보인다. 그리고 준지도 분류에서 사용하는 것처럼 반응 값이 없는 자료의 초기추정은 작은 값을 가지는 평활계수를 사용하여 과적합 (overfitting)되도록 하는 것이 좋음을 증명한다.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.467-484
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• 2022

In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre's K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence.

• International Journal of Aeronautical and Space Sciences
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• 제2권1호
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• pp.1-11
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• 2001

The time implicit point SGS scheme is applied to compute hypersonic viscous flows in thermochemical nonequilibrium. The performance of the point SGS scheme is then compared with those of the line SGS and the LU-SGS schemes. Comparison of convergence histories with the effect of multiple forward and backward sweeps are made for the flow over a 2D cylinder experimentally studied by Hornung and the flow over a hemisphere at conditions corresponding to the peak heating condition during the reentry flight of an SSTO vehicle. Results indicate that the point SGS scheme with multiple sweeps is as robust and efficient as the line SGS scheme. For the point SGS and the LU-SGS scheme, the rate of improvement in convergence is largest with two sweep cycles. However, for the line SGS scheme, it is found that more than one sweep cycle deteriorates the convergence rate.

• 호남수학학술지
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• 제39권1호
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• pp.1-25
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• 2017

In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

• Communications for Statistical Applications and Methods
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• 제3권3호
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• pp.271-282
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• 1996

this paper deal with the estimation of the power spectral density function of time series. A kernel estimator which is based on local average is defined and the rates of convergence of the pointwise, $$L_2$-norm; and; $L{\infty}$-norm associated with the estimator are investigated by restricting as to kernels with suitable assumptions. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for 0$N^{-r}$ both in the pointwiseand $$L_2$-norm, while; $N^{r-1}(logN)^{-r}$is the optimal rate in the $L{\infty}-norm$. Some examples are given to illustrate the application of main results.

• 한국음향학회지
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• 제15권5호
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• pp.30-37
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• 1996

통신 시스템에서 LMS 알고리즘을 이용하여 설계한 적응 등화기는 구조의 간단함과 효율성에 비해 수렴 속도가 느린 단점이 있다. 본 논문에서는 이러한 단점을 보완하기 위해 웨이브렛 변환 평면에서 적응 동기화를 설계하여 채널의 왜곡정도와 필터 차수의 변화에 따른 수렴 속도를 시평면 LMS 알고리즘을 이용해 설계한 등화기와 비교하였다. 시뮬레이션결과 웨이브렛 평면에서의 적응 등화기가 기존의 등화기보다 우수한 성능 향상을 보였다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제17권3호
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• pp.816-839
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• 2023

In a random vector functional link (RVFL) network, shortcomings such as local optimal stagnation and decreased convergence performance cause a reduction in the accuracy of illumination correction by only inputting the weights and biases of hidden neurons. In this study, we proposed an improved regularized random vector functional link (RRVFL) network algorithm with an optimized grey wolf optimizer (GWO). Herein, we first proposed the moth-flame optimization (MFO) algorithm to provide a set of excellent initial populations to improve the convergence rate of GWO. Thereafter, the MFO-GWO algorithm simultaneously optimized the input feature, input weight, hidden node and bias of RRVFL, thereby avoiding local optimal stagnation. Finally, the MFO-GWO-RRVFL algorithm was applied to ameliorate the performance of illumination correction of various test images. The experimental results revealed that the MFO-GWO-RRVFL algorithm was stable, compatible, and exhibited a fast convergence rate.

• 대한수학회보
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• 제50권3호
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• pp.823-832
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• 2013

We present a new algorithm for solving a system of nonlinear equations with convex constraints which combines proximal point and projection methodologies. Compared with the existing projection methods for solving the problem, we use a different system of linear equations to obtain the proximal point; and moreover, at the step of getting next iterate, our projection way and projection region are also different. Based on the Armijo-type line search procedure, a new hyperplane is introduced. Using the separate property of hyperplane, the new algorithm is proved to be globally convergent under much weaker assumptions than monotone or more generally pseudomonotone. We study the convergence rate of the iterative sequence under very mild error bound conditions.

• 호남수학학술지
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• 제44권2호
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• pp.281-295
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• 2022

This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.