• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.301-311
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• 2015

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al. [8, 9]. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems [1].

• 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.

• East Asian mathematical journal
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• v.19 no.1
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• pp.17-26
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• 2003

This paper demonstrates the CAS technique of analyzing the nature and the structure of the numerical error for education and research purposes. This also illustrates the CAS approach in experimenting with the numerical operations in an arbitrary computer number system and also in doing error analysis in a visual manner.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.809-823
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• 2015

This paper is devoted to presenting a MacWilliams type identity for m-spotty RT weight enumerators of byte error control codes over finite commutative Frobenius rings, which can be used to determine the error-detecting and error-correcting capabilities of a code. This provides the relation between the m-spotty RT weight enumerator of the code and that of the dual code. We conclude the paper by giving three illustrations of the results.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.741-754
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• 2002

In this paper we present an error bound for cubic spline approximation of conic section curve. We compare it to the error bound proposed by Floater [1]. The error estimating function proposed in this paper is sharper than Floater's at the mid-point of parameter, which means the overall error bound is sharper than Floater's if the estimating function has the maximum at the midpoint.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.475-486
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• 2011

The paper deals with repeated low-density burst error detecting codes with a specied weight or less. Linear codes capable of detecting such errors have been studied. Further codes capable of correcting and simultaneously detecting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.425-444
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• 2021

In this study, under the assumption that the goal pursued in measurement area can be reached through the composition of the measurement activity considering the mathematical process, the method of summing the interior angles of a triangle using the measurement error was applied to the 4th grade class of the elementary school. Results of the study, first, students were able to recognize the possibility of measurement error by learning the sum of the interior angles of a triangle using the measurement error. Second, the discussion process based on the measurement error became the basis for students to attempt mathematical justification. Third, the manipulation activity using the semicircle was recognized as a natural and intuitive way of mathematical justification by the students and led to generalization. Fourth, the method of guiding the sum of the interior angles of a triangle using the measurement error contributed to the development of students' mathematical communication skills and positive attitudes toward mathematics.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.459-471
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• 2002

In applications using a linear regression model with nested error structure, one might be interested in making inferences concerning variance components. This article proposes approximate confidence intervals on the variance component of the primary level in a simple linear regression model with an unbalanced nested error structure. The intervals are compared using computer simulation and recommendations are provided for selecting an appropriate interval.

• Honam Mathematical Journal
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• v.9 no.1
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• pp.99-111
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• 1987

In this paper we shall construct a ridge estimator in a multiple linear model with the correlated error structure. The existence of the biasing parameter satisfying the Mean Squared Error Criterion is also proved. Furthermore, we shall determine the value of shrinkage factors by the iteration method.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.835-844
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• 2007

This paper considers the problem of estimating the error distribution function in nonparametric regression models. Sufficient conditions are given under which the kernel estimator of the error distribution function based on nonparametric residuals satisfies the law of iterated logarithm.