• Title, Summary, Keyword: interpolating

### APPROXIMATION AND BALANCING ORDERS FOR TOTALLY INTERPOLATING BIORTHOGONAL MULTIWAVELET SYSTEMS

• Choi, Young-Woo;Jung, Jae-Won
• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1157-1167
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• 2011
• We consider totally interpolating biorthogonal multiwavelet systems with finite impulse response two-band multifilter banks, a study balancing order conditions of such systems. Based on FIR and interpolating properties, we show that approximation order condition is completely equivalent to balancing order condition. Consequently, a prefiltering can be avoided if a totally interpolating biorthogonal multiwavelet system satisfies suitable approximation order conditions. An example with approximation order 4 is provided to illustrate the result.

### An Efficient Adaptive Wavelet-Collocation Method Using Lifted Interpolating Wavelets (수정된 보간 웨이블렛응 이용한 적응 웨이블렛-콜로케이션 기법)

• Kim, Yun-Yeong;Kim, Jae-Eun
• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8
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• pp.2100-2107
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• 2000
• The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

### Piecewise Lagrange 보간다항식의 특성에 관한 연구

• Yun, Gyeong-Hyeon
• ETRI Journal
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• v.6 no.2
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• pp.18-26
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• 1984
• Among the various forms of interpolating polynomial for approximation, this paper is a study about the characteristics of piecewise Lagrange interpolating polynomials. And throughout the study, an attempt is made to construct the two-dimensional ap proximating function over Rectangular Grid and Triangular Grid by using the one-dim ensional interpolating polynomials.

### INFINITUDE OF MINIMALLY SUPPORTED TOTALLY INTERPOLATING BIORTHOGONAL MULTIWAVELET SYSTEMS WITH LOW APPROXIMATION ORDERS

• Choi, Youngwoo;Jung, Jaewon
• Korean Journal of Mathematics
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• v.21 no.3
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• pp.247-263
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• 2013
• By analyzing one-parameter families of totally interpolating multiwavelet systems of minimal total length with low approximation orders, whose explicit formulas were obtained with the aid of well-known relations of filters, we demonstrate the infinitude of such systems.

### APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASS

• Akgun Ramazan;Israfilov Daniyal M.
• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.413-424
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• 2006
• Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

### Multipliers on the dirichlet space $D(Omega)$

• Nah, Young-Chae
• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.633-642
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• 1995
• Recently S. Axler proved that every sequence in the unit disk U converging to the boundary contains an interpolating subsequence for the multipliers of the Dirichlet space D(U). In this paper we generalizes Axler's result to the finitely connected planer domains such that the Dirichlet spaces are contained in the Bergman spaces.

### Improved Interpolating Equation for Industrial Platinum Resistance Thermometer (산업용 백금저항온도계를 위한 향상된 내삽식)

• Yang, In-Seok;Kim, Yong-Gyoo;Gam, Kee-Sool;Lee, Young-Hee
• Journal of Sensor Science and Technology
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• v.21 no.2
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• pp.109-113
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• 2012
• We propose an improved interpolating equation to express temperature-resistance characteristics for modern industrial platinum resistance thermometers (PRTs). Callendar-van Dusen equation which has been widely used for platinum resistance thermometer fails to fully describe temperature characteristics of high quality PRTs and leaves systematic residual when the calibration point include temperatures above $300^{\circ}C$. Expanding Callendar-van Dusen to higher-order polynomial drastically improves the uncertainty of the fitting even with reduced degrees of freedom of the fitting. We found that in the fourth-order polynomial fitting, the third-order and fourth-order coefficients have a strong correlation. Using the correlation, we suggest an improved interpolating equation in the form of fourth-order polynomial, but with three fitting parameters. Applying this interpolating equation reduced the uncertainty of the fitting to 32 % of that resulted from the traditional Callendar-van Dusen. This improvement was better than that from a simple third-order polynomial despite that the degrees of the freedom of the fitting was the same.

### Performance Estimation Based on 4D Lookup Table Interpolating and Unit Cell Discharge Tests for Thermal Battery (4D Lookup Table Interpolating을 이용한 단위 전지 방전 시험 기반 열전지 성능 예측)

• Park, Byeong June;Kim, Ji Youn;Ha, Sang Hyeon;Cho, Jang Hyeon
• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.30 no.6
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• pp.393-400
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• 2017
• For comparison to the Li-ion battery, evaluating a thermal battery must consider additional variables. The first one is the temperature difference between the battery and its unit cell. Thermal batteries and their unit cells have a temperature difference that is caused by the thermal battery activation mechanism and its shape. The second variable is the electrochemical reaction steps. Most Li-ion batteries have a constant electrochemical reaction at the electrode, and battery voltage is affected when the concentration of Li ions is changed. However, a thermal battery has several steps in its electrochemical reaction, and each step has a different potential. In this study, we used unit cell discharge tests based on interpolating a 4D lookup table to estimate the performance of a thermal battery. From the test results, we derived an estimation algorithm by interpolating the table, which is queried from specified profile groups. As a result, we found less than a 5 percent difference between estimation and experiment at the 1.3 V cut-off time.

### Nonlinear Function Approximation by Fuzzy-neural Interpolating Networks

• Suh, Il-Hong;Kim, Tae-Won-
• Proceedings of the Korean Institute of Intelligent Systems Conference
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• pp.1177-1180
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• 1993
• In this paper, a fuzzy-neural interpolating network is proposed to efficiently approximate a nonlinear function. Specifically, basis functions are first constructed by Fuzzy Membership Function based Neural Networks (FMFNN). And the fuzzy similarity, which is defined as the degree of matching between actual output value and the output of each basis function, is employed to determine initial weighting of the proposed network. Then the weightings are updated in such a way that square of the error is minimized. To show the capability of function approximation of the proposed fuzzy-neural interpolating network, a numerical example is illustrated.

### An 8-b, 40-MS/s, Folding and Interpolating ADG for Ultrasound Imaging System (초음파진단기용 8-b, 40-Ms/s, Folding and Interpolating A/D 변환기의 설계)

• Ryu, Seung-Tak;Lee, Byung-Woo;Hong, Young-Wook;Choi, Bea-Geun;Cho, Gyu-Hyeong
• Proceedings of the KIEE Conference
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• pp.3178-3180
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• 1999
• 초음파 진단기의 신호처리에 필요한 8-b 해상도와 40MS/s 이상의 변환속도를 갖는 ADC를 Folding and Interpolating 형태로 설계했다. 전력소모와 입력단의 오프셋에 의한 영향을 줄이기 위해 프리엠프의 출력을 Interpolation하여 그 개수를 절반으로 줄임으로써 전력소모를 줄였고, 기존의 전압모드 Interpolation 회로에서의 단순한 source follower를 정궤환을 이용한 버퍼의 형태로 바꾸어 이득을 개선시킴으로써 전압의 이용율을 높일 수 있었다. ADC에서 가장 중요한 비교기를 설계함에 있어서는 다이나믹 전력 소모만 있는 구조에 킥-백 노이즈를 줄이기 위한 설계를 했다 $0.6{\mu}m$ CMOS 공정을 이용해 설계되었고, Layout 결과 칩의 면적은 $1.3mm{\times}1.3mm$. 모의 실험결과 40MS/s에서 70mw의 전력을 소모하였다.