• Structural Engineering and Mechanics
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• v.30 no.2
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• pp.225-245
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• 2008

T-splines are recently proposed mathematical tools for geometric modeling, which are generalizations of B-splines. Local refinement can be performed effectively using T-splines while it is not the case when B-splines or NURBS are used. Using T-splines, patches with unmatched boundaries can be combined easily without special techniques. In the present study, an analysis framework using T-splines is proposed. In this framework, T-splines are used both for description of geometries and for approximation of solution spaces. This analysis framework can be a basis of a CAD/CAE integrated approach. In this approach, CAD models are directly imported as the analysis models without additional finite element modeling. Some numerical examples are presented to illustrate the effectiveness of the current analysis framework.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.47-53
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• 2010

In this paper we propose a new type of splines-biquadratic submesh splines over hierarchical T-meshes. The biquadratic submesh splines are in rational form consisting of some biquadratic B-splines defined over tensor-product submeshes of a hierarchical T-mesh, where every submesh is around a cell in the crossing-vertex relationship graph of the T-mesh. We provide an effective algorithm to locate the valid tensor-product submeshes. A local refinement algorithm is presented and the application of submesh splines in surface fitting is provided.

• Journal of Multimedia Information System
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• v.5 no.1
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• pp.63-66
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• 2018

In this work, the smoothing and the interpolation basis splines are analyzed. As well as the possibility of using the spectral properties of the basis splines for digital signal processing are shown. This takes into account the fact that basic splines represent finite, piecewise polynomial functions defined on compact media.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.2
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• pp.127-134
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• 2009

T-splines are recently proposed geometric modeling tools. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. Local refinement can be performed very easily for T-splines while it is limited for B-splines or NURBS. Using T-splines, patches with unmatched boundaries can be combined easily without special technique. In this study, the analysis methodology using T-splines is proposed. In this methodology, T-splines are used both for description of geometries and for approximation of solution spaces. Two-dimensional linear elastic and dynamic problems will be solved by employing the proposed T-spline finite element method, and the effectiveness of the current analysis methodology will be verified.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.47-53
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• 2001

A problem of approximation by irrational splines is considered. These splines have a constant curvature between interpolation nodes and need only one additional boundary condition for derivatives, which should be set only at one of two boundary nodes, that is impossible for usual polynomial splines required boundary conditions at both boundary nodal points. Some estimations for numerical differentiation and rounding error analysis are presented.

• 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.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.165-176
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• 1997

In order to overcome computational ill-posedness which arises when we solve the least square problems, nonlinear smoothing splines are used. The existence and the convergence on nonlinear smoothing spline are shown with numerical experiments.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.955-982
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• 1996

In surface compression applications, one of the main issues is how to efficiently store and calculate the computer representation of certain surfaces. This leads us to consider a nonlinear approximation by box splines with free knots since, for instance, the nonlinear method based on wavelet decomposition gives efficient compression and recovery algorithms for such surfaces (cf. [12]).

• Asia pacific journal of information systems
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• v.11 no.1
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• pp.61-73
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• 2001

Predicting a variable using other variables in a large data set is a very difficult task. It involves selecting variables to include in a model and determining the shape of the relationship between variables. Nonparametric regression such as smoothing splines and neural networks are widely-used methods for such a task. We propose an alternative method based on a genetic algorithm(GA) to solve this problem. We applied GA to regression splines, a nonparametric regression method, to estimate functional forms between variables. Using several simulated and real data, our technique is shown to outperform traditional nonparametric methods such as smoothing splines and neural networks.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.17-19
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• 2005

In this paper, using B-splines as universial approximators, we have obtained a plant parametrization which permits the construction of an adaptive observer. The particular property of this parametrization is that the dynamic order of the filters in this design does not depend on the number of parameters in the plant parametrization. This appears to be a beneficial property especially because the number of such parameters tends to be very high for universial approximator based designs.