• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.3
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• pp.89-95
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• 1997

This paper examines the relation between multidimensional linear interpolation (MDI) and regularization net-works, and shows that an MDI is a special form of regularization networks. For this purpose we propose a triangular basis function(TBF) network. Also we verified the condition when our proposed TBF becomes a well-known radial basis function (RBF).

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.4
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• pp.34-38
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• 1996

This paper examines the relation between multidimensional linear interpolation(MDI) and fuzzy reasoning, and shows that an MDI is a special form of Tsukamoto's fuzzy reasoning. From this result, we found new possibility of defuzzification strategy.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1847-1852
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• 2004

This article provides the connection between feedback stabilization and interpolation conditions for n-D linear systems (n > 1). In addition to internal stability, if one demands performance as a design goal, then there results an n-D matrix Nevanlinna-Pick interpolation problem. Application of recent work on Nevanlinna-Pick interpolation on the polydisk yields a solution of the problem for the 2-D case. The same analysis applies in the n-D case (n > 2), but leads to solutions which are contractive in a norm (the "Schur-Agler norm") somewhat stronger than the $H^{\infty}$ norm. This is an analogous version of the connection between the standard $H^{\infty}$ control problem and an interpolation problem of Nevanlinna-Pick type in the classical 1-D linear time-invariant systems.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.562-567
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• 1998

This paper examined the relations among the multidimensional linear interpolation(MDI) and fuzzy reasoning , and neural networks, and showed that an showed that an MDI is a special form of Tsukamoto's fuzzy reasoning and regularization networks in the perspective of fuzzy reasoning and neural networks, respectively. For this purposes, we proposed a special Tsukamoto's membership (STM) systemand triangular basis function (TBF) networks, Also we verified the condition when our proposed TBF becomes a well-known radial basis function (RBF).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.147-150
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• 1996

This paper examines the realtionship between Multidimensional linear interpolation (MDI) and fuzzy reasoning, and shows that an MDI is a special form of Tsukamoto's fuzzy reasoning. From this result, we find a new possibility of defuzzification scheme.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.11a
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• pp.128-133
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• 1997

This paper examines the relation between multidimensional linear interpolation ( MDI ) and regularization networks, and shows that and MDI is a special form of regularization networks. For this purpose we propose a triangular basis function ( TBF ) network. Also we verified the condition when our proposed TBF becomes a well-known radial basis function ( RBF ).

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).

• Korean Journal of Computational Design and Engineering
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• v.10 no.5
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• pp.314-327
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• 2005

This paper describes the volumetric data modeling and analysis methods that employ volumetric NURBS or VNURBS that represents heterogeneous objects or fields in multidimensional space. For volumetric data modeling, we formulate the construction algorithms involving the scattered data approximation and the curvilinear grid data interpolation. And then the computational algorithms are presented for the geometric and mathematical analysis of the volume data set with the VNURBS model. Finally, we apply the modeling and analysis methods to various field applications including grid generation, flow visualization, implicit surface modeling, and image morphing. Those application examples verify the usefulness and extensibility of our VNUBRS representation in the context of volume modeling and analysis.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.185-209
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• 2022

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.69-93
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• 2023

Here we give multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized Gudermannian sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.