• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1299-1316
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• 2010

We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.192-197
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• 2000

In CNC machining, a free curve is cut into small linear segments using the linear interpolation(G01) method. Therefore, the interpolation error along the curve is not constant due to the changing curvature. This paper presents a NURBS (Non-Uniform Rational B-Spline) interpolation algorithm for machining free curves with high precision and high speed. The proposed NURBS interpolation defines the tool path with NURBS parameters and limits the interpolation error to any desired level by adjusting the feed rate considering the curvature of the shape and sampling time. Both linear and NURBS interpolations are compared to show the validity of the proposed algorithm.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.9-18
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• 1996

This study examines effect of various interpolations of interior control function for analytic methods such as Thomas-Middlecoff and Sorenson methods. Laplace interpolation is developed and compared among linear interpolation and exponential interpolation systematically.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.104-109
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• 1995

This study examines effect of various interpolations of interior control function for analytic methods such as Thomas-Middlecoff and Sorenson methods. Laplace interpolation is developed and compared among linear interpolation and exponential interpolation systematically.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.177-196
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• 2008

Using the results on the coefficients of Hermite-Fej$\acute{e}$r interpolations in [5], we investigate convergence of Hermite and Hermite-$Fej{\acute{e}}r$ interpolation of order m, m=1,2,... in $L_p(0<p<{\infty})$ and associated product quadrature rules for a class of fast decaying even $Erd{\H{o}}s$ weights on the real line.

• The KIPS Transactions:PartA
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• v.18A no.6
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• pp.249-254
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• 2011

This paper describes an efficient design of the interpolation circuit to generate the luma and chroma sub-pixels for H.264 motion estimation. The circuit based on the proposed architecture does not require any input data buffering and processes the horizontal, vertical and diagonal sub-pixel interpolations in parallel. The performance of the circuit is further improved by simultaneously processing the 1/2-pixel and 1/4-pixel interpolations for luma components and the 1/8-pixel interpolations for chroma components. In order to reduce the circuit size, we store the intermediate data required to process all the interpolations in parallel in the internal SRAM's instead of registers. We described the proposed circuit at register transfer level and verified its operation on FPGA board. We also synthesized the gate-level circuit using 130nm CMOS standard cell library. It consists of 20,674 gates and has the maximum operating frequency of 244MHz. The total number of SPSRAM bits used in our circuit is 3,232. The size of our circuit (including logic gates and SRAM's) is smaller than others and the performance is still comparable to them.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1078-1083
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• 2004

We proposed a method to compensate incomplete observations and made a study of environmental problem, water quality of Tama-River in Tokyo.The method is based on interpolations of the multi-layer neural networks. We call the approach as CQSAR method .which can compensate the defect data.The water quality data include defects which will give wrong effect to other normal data. The CQSAR method suppresses the wrong effect .Thus, we believe that the proposed CQSAR method has practical usability for environment examinations.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.121-133
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• 2008

In this article, we define Minkowski Pythagorean-hodograph (MPH) curves in the Minkowski plane $\mathbb{R}^{1,1}$ and obtain $C^1$ Hermite interpolations for MPH quintics in the Minkowski plane $\mathbb{R}^{1,1}$. We also have the envelope curves of MPH curves, and make surfaces of revolution with exact rational offsets. In addition, we present an example of $C^1$ Hermite interpolations for MPH rational curves in $\mathbb{R}^{2,1}$ from those in $\mathbb{R}^{1,1}$ and a suitable MPH preserving mapping.

• 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).

• 한국가시화정보학회:학술대회논문집
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• 2004.12a
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• pp.47-55
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• 2004

Several interpolations for image deformation in PIV were evaluated. The tested interpolation methods are linear, quadratic, truncated sinc, windowed sinc, cubic, Lagrange, Gaussian $2^{nd}\;and\;6^{th}$ interpolators. Bias errors and random errors were evaluated in the range of $0\~3.0$ pixel uniform displacement using synthetic images. We also measured the time cost of each interpolator with respect to kernel size. The cubic interpolator with $6\times6$ kernel showed the best results in terms of the performance and time cost.