• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.735-748
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• 1998

We analyze the error in the p version of the of the finite element method when the effect of the quadrature error is taken in the load vector. We briefly study some results on the $H^{1}$ norm error and present some new results for the error in the $L^{2}$ norm. We inves-tigate the quadrature error due to the numerical integration of the right hand side We present theoretical and computational examples showing the sharpness of our results.

• The Journal of the Acoustical Society of Korea
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• v.16 no.3E
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• pp.62-68
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• 1997

In this paper, a modified adaptive sign (MAS) algorithm based on a mixed norm error criterion is proposed. The mixed norm error criterion of be minimized is constructed as a combined convex function of the mean-absolute error and the mean-absolute error to the third power. A convergence analysis of the MAS algorithm is also presented. Under a set of mild assumptions, a set of nonlinear evolution equations that characterizes the statistical mean and mean-squared behavior of the algorithm is derived. Computed simulations are carried out to verify the validity of our derivations.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.91-94
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• 2001

Recently a constant-norm constraint equation-error method was proposed to solve the bias problem in adaptive IIR filtering. However, the method adopts a fixed step-size and thus results in slow convergence for a small step-size and significant misadjustment error for a largestep-size. In this paper, we propose a variable step-size (VSS) algorithm that greatly improves convergence properties of the constant-norm constraint equation-error method. The analysis and the simulation results show that the proposed method indeed achieves both fast convergence and small misadjustment error.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.125-130
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• 2007

We propose a simple and intuitive method to derive the exact convergence rate of global $L_{2}-norm$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $M{\"u}ller-Gronbach\;(2004)$. We conclude that any strong numerical scheme of order ${\gamma}\;>\;1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.

• Journal of the Korean Geotechnical Society
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• v.40 no.4
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• pp.127-135
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• 2024

The purpose of this paper is to establish the relationship between compression wave velocity and porosity in unsaturated soil using a deep neural network (DNN) algorithm. Input parameters were examined using the error norm method to assess their impact on porosity. Compression wave velocity was conclusively found to have the most significant influence on porosity estimation. These parameters were derived through both field and laboratory experiments using a total of 266 numerical data points. The application of the DNN was evaluated by calculating the mean squared error loss for each iteration, which converged to nearly zero in the initial stages. The predicted porosity was analyzed by splitting the data into training and validation sets. Compared with actual data, the coefficients of determination were exceptionally high at 0.97 and 0.98, respectively. This study introduces a methodology for predicting dependent variables through error norm analysis by disregarding fewer sensitive factors and focusing on those with greater influence.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.621-637
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• 2005

A hybrid method solving regularized structured linear total least norm (RSTLN) problems, which have highly ill-conditioned coefficient matrix with special structures, is suggested and analyzed. This scheme combining RSTLN algorithm and separation by parts guarantees the convergence of parameters and has an advantages in reducing the residual norm and relative error of solutions. Computational tests for problems arisen in signal processing and image formation process confirm that the presenting method is effective for more accurate solutions to (R)STLN problem than the (R)STLN algorithm.

• East Asian mathematical journal
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• v.31 no.5
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• pp.685-693
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• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.461-464
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• 2003

This paper proposes the multi-level vector error diffusion for smear artifact reduction in the boundary regions. Smear artifact mainly results from a large accumulation of quantization error. Accordingly, to reduce these artifacts, the proposed method excludes the large quantization error in the error diffusion process by comparing the magnitude of the error vector with predetermined first threshold. In addition, if the vector norm of the difference between the error adjusted input vector and the primary co]or that has minimum vector norm for the error adjusted input vector is larger than second threshold, the error is excluded. As a result, the proposed method reduce smear artifact in the boundary region and produces visually pleasing halftone pattern.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.707-719
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• 2014

In this paper, we investigate a variational discretization approximation of elliptic optimal control problems with control constraints. The state and the co-state are approximated by piecewise linear functions, while the control is not directly discretized. By using some proper intermediate variables, we derive a second-order convergence in $L^2$-norm and superconvergence between the numerical solution and elliptic projection of the exact solution in $H^1$-norm or the gradient of the exact solution and recovery gradient in $L^2$-norm. Then we construct a posteriori error estimates by using the superconvergence results and do some numerical experiments to confirm our theoretical results.