• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.483-490
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• 1995

A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

• Journal of information and communication convergence engineering
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• v.9 no.4
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• pp.424-427
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• 2011

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines, of Reyabenko's splines and results of simulink-modeling is presented. The advantages of this paper is that we comprise the basic spline with classical polynomials both on accuracy, as well as degree of paralleling calculations are also show's.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1848-1853
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• 1991

To solve the nonlinear system problems, many methods have been proposed. Generally those methods however need long processing time because of their complicated algorithms. On the other hand, some simple linearization methods also have been studied. In this paper, a new linearization method using cubic splines[1] is proposed. The approximated linear system obtained by this method we can apply the conventional simple linear system theories such as Kalman filter[2, 3] for the estimation problem.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2010.04a
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• pp.415-417
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• 2010

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.759-770
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• 1998

In this paper we use uniform cubic spline polynomials to derive some new consistency relations. These relations are then used to develop a numerical method for computing smooth approxi-mations to the solution and its first second as well as third derivatives for a second order boundary value problem. The proesent method out-performs other collocations finite-difference and splines methods of the same order. numerical illustratiosn are provided to demonstrate the practical use of our method.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.89-98
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• 2011

The Fourier series has a rapid oscillation near end points at jump discontinuity which is called the Gibbs phenomenon. There is an overshoot (or undershoot) of approximately 9% at jump discontinuity. In this paper, we prove that a bunch of series representations (certain nonharmonic Fourier series) give good approximations vanishing Gibbs phenomenon. Also we have an application for approximating some shape of upper part of a vehicle in a different way from the method of cubic splines and wavelets.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.525-538
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• 1996

In the course of working on the preconditioning of $C^1$-bicubic collocation method, one has to deal with the $C^1$-bicubic splines. In this paper we are concerned with $C^1$-bicubic spline interpolant for a given function. We construct a basis for the space of $C^1$-bicubic splines for a given partition and find the $C^1$-bicubic spline interpolant for a given function defined on a set.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.57-76
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• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.569-573
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• 2001

An approximate representation of discrete functions {f$_{i,j}\mid$｜i, j=-1, 0, 1, …, N+1}in two variables by a fuzzy system is described. We use the cubic B-splines as fuzzy sets for the input fuzzification and spike functions as the output fuzzy sets. The ordinal number of f$_{i,j}$ in the sorted list is taken to be the out put fuzzy set number in the (i, j) th entry of the fuzzy rule table. We show that the fuzzy system is an exact representation of the cubic spline function s(x, y)=$\sum_{N+1}^{{i,j}=-1}f_{i,j}B_i(x)B_j(y)$ and that the approximation error S(x, y)-f(x, y) is surprisingly O($h^2$) when f(x, y) is three times continuously differentiable. We prove that when f(x, y) is a gray scale image, then the fuzzy system is a smoothed representation of the image and the original image can be recovered exactly from its fuzzy system representation when it is a digitized image.e.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.1 no.1
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.