• Title, Summary, Keyword: mixed interpolation

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On A Symbolic Method for Error Estimation of a Mixed Interpolation

  • Thota, Srinivasarao
    • Kyungpook Mathematical Journal
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    • v.58 no.3
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    • pp.453-462
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    • 2018
  • In this paper, we present a symbolic formulation of the error obtained due to an approximation of a given function by the mixed-interpolating function. Using the proposed symbolic method, we compute the error evaluation operator as well as the error estimation at any arbitrary point. We also present an algorithm to compute an approximation of a function by the mixed interpolation technique in terms of projector operator. Certain examples are presented to illustrate the proposed algorithm. Maple implementation of the proposed algorithm is discussed with sample computations.

A 4x Time-Domain Interpolation 6-bit 3.4 GS/s 12.6 mW Flash ADC in 65 nm CMOS

  • Liu, Jianwei;Chan, Chi-Hang;Sin, Sai-Weng;U, Seng-Pan;Martins, Rui Paulo
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.16 no.4
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    • pp.395-404
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    • 2016
  • A 6-bit 3.4 GS/s flash ADC in a 65 nm CMOS process is reported along with the proposed 4x time-domain interpolation technique which allows the reduction of the number of comparators from the conventional $2^N-1$ to $2^{N-2}$ in a N-bit flash ADC. The proposed scheme effectively achieves a 4x interpolation factor with simple SR-latches without extra clocking and calibration hardware overhead in the interpolated stage where only offset between the $2^{N-2}$ comparators needs to be calibrated. The offset in SR-latches is within ${\pm}0.5$ LSB in the reported ADC under a wide range of process, voltage supply, and temperature (PVT). The design considerations of the proposed technique are detailed in this paper. The prototype achieves 3.4 GS/s with 5.4-bit ENOB at Nyquist and consumes 12.6 mW power at 1 V supply, yielding a Walden FoM of 89 fJ/conversion-step.

Optimal Interpolation Functions of 2-None Hybrid-Mixed Curved Beam Element (두 절점 혼합 곡선 보요소의 보간함수 선정)

  • Kim, Jin-Gon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.12
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    • pp.3003-3009
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    • 2000
  • In this paper, we propose a new efficient hybrid-mixed C(sup)0 curved beam element with the optimal interpolation functions determined from numerical tests, which gives very accurate locking-free two-node curved beam element. In the element level, the stress parameters are eliminated from the stationary condition and the nodeless degrees of freedom are also removed by static condensation so that a standard six-by-six stiffness matrix is finally obtained. The numeri cal benchmark problems show that the element with cubic displacement functions and quadratic stress functions is the most efficient.

TWO-SCALE PRODUCT APPROXIMATION FOR SEMILINEAR PARABOLIC PROBLEMS IN MIXED METHODS

  • Kim, Dongho;Park, Eun-Jae;Seo, Boyoon
    • Journal of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.267-288
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    • 2014
  • We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order $L^{\infty}((0, T];L^2({\Omega}))$-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.

RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF MIXED FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS

  • Chen, Yanping;Huang, Yunqing;Hou, Tianliang
    • Journal of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.549-569
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    • 2012
  • In this paper asymptotic error expansions for mixed finite element approximations to a class of second order elliptic optimal control problems are derived under rectangular meshes, and the Richardson extrapolation of two different schemes and interpolation defect correction can be applied to increase the accuracy of the approximations. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators of the mixed finite element method for optimal control problems.

$H^{\infty}$ Optimization of Mixed Sensitivity Function using Model-Matching and Interpolation Algorithm (모델정합과 보간 알고리즘을 이용한 혼합된 감도함수의 $H^{\infty}$ 최적화)

  • 윤한오;박홍배
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.29B no.3
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    • pp.16-24
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    • 1992
  • In this paper, we solve the problem of designing a robust optimal controller which minimizes the H$\infty$-norm of the mixed sensitivity function matrix for linear multivariable systems. For a given minimized value, ${\gamma}$>o, an algorithm of finding all stabilizing controllers, such that the H$\infty$-norm of the mixed sensitivity function matrix is less than ${\gamma}$, is developed. The proposed algorithm, which is based on the model-matching and the interpolation theory, can be used for the H$\infty$-optimization problem.

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Computation of 2-D mixed-mode stress intensity factors by Petrov-Galerkin natural element method

  • Cho, Jin-Rae
    • Structural Engineering and Mechanics
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    • v.56 no.4
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    • pp.589-603
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    • 2015
  • The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CS-FE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.

Fast Multiple Mixed Image Interpolation Method for Image Resolution Enhancement (영상 해상도 개선을 위한 고속 다중 혼합 영상 보간법)

  • Kim, Won-Hee;Kim, Jong-Nam;Jeong, Shin-Il
    • Journal of Broadcast Engineering
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    • v.19 no.1
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    • pp.118-121
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    • 2014
  • Image interpolation is a method of determining the value of new pixel coordinate in the process of image scaling. Recently, image contents are likely to be a large-capacity, interpolation algorithm is required to generate fast enhanced result image. In this paper, fast multiple mixed image interpolation for image resolution enhancement is proposed. The proposed method estimates expected 12 shortfalls from four sub-images of a input image, and generates the result image that is interpolated in the combination of the expected shortfalls with the input image. The experimental results demonstrate that PSNR increases maximum value of 1.9dB, SSIM increases maximum value of 0.052, and the subjective quality is superior to any other compared methods. Moreover, it is known by algorithm running time comparison that the proposed method has been at least three times faster than the compared conventional methods. The proposed method can be useful for application on image resolution enhancement.

Development of FAMD Code to Calculate the Fluid Added Mass and Damping of Arbitrary Structures Submerged in Confined Viscous Fluid

  • Koo, Gyeong-Hoi;Lee, Jae-Han
    • Journal of Mechanical Science and Technology
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    • v.17 no.3
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    • pp.457-466
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    • 2003
  • In this paper, the numerical finite element formulations were derived for the linearized Navier-Stokes' equations with assumptions of two-dimensional incompressible, homogeneous viscous fluid field, and small oscillation and the FAMD (Fluid Added Mass and Damping) code was developed for practical applications calculating the fluid added mass and damping. In formulations, a fluid domain is discretized with C$\^$0/-type quadratic quadrilateral elements containing eight nodes using a mixed interpolation method, i.e., the interpolation function for the velocity variable is approximated by a quadratic function based on all eight nodal points and the interpolation function for the pressure variable is approximated by a linear function based on the four nodal points at vertices. Using the developed code, the various characteristics of the fluid added mass and damping are investigated for the concentric cylindrical shell and the actual hexagon arrays of the liquid metal reactor cores.

Barycentric Approximator for Reinforcement Learning Control

  • Whang Cho
    • International Journal of Precision Engineering and Manufacturing
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    • v.3 no.1
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    • pp.33-42
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    • 2002
  • Recently, various experiments to apply reinforcement learning method to the self-learning intelligent control of continuous dynamic system have been reported in the machine learning related research community. The reports have produced mixed results of some successes and some failures, and show that the success of reinforcement learning method in application to the intelligent control of continuous control systems depends on the ability to combine proper function approximation method with temporal difference methods such as Q-learning and value iteration. One of the difficulties in using function approximation method in connection with temporal difference method is the absence of guarantee for the convergence of the algorithm. This paper provides a proof of convergence of a particular function approximation method based on \"barycentric interpolator\" which is known to be computationally more efficient than multilinear interpolation .