• Kyungpook Mathematical Journal
• /
• 제58권3호
• /
• pp.453-462
• /
• 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.

• JSTS:Journal of Semiconductor Technology and Science
• /
• 제16권4호
• /
• pp.395-404
• /
• 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.

• 대한기계학회논문집A
• /
• 제24권12호
• /
• pp.3003-3009
• /
• 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.

• 대한수학회지
• /
• 제49권3호
• /
• pp.549-569
• /
• 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.

• 대한수학회지
• /
• 제51권2호
• /
• pp.267-288
• /
• 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.

• 전자공학회논문지B
• /
• 제29B권3호
• /
• pp.16-24
• /
• 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.

• Structural Engineering and Mechanics
• /
• 제56권4호
• /
• pp.589-603
• /
• 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.

• 방송공학회논문지
• /
• 제19권1호
• /
• pp.118-121
• /
• 2014

영상 보간법은 영상의 크기 변환에서 나타나는 새로운 좌표의 화소의 값을 결정하는 방법이다. 영상 콘텐츠가 대용량화되면서 고속으로 개선된 결과 영상을 생성할 수 있는 영상 보간법이 요구된다. 따라서 본 논문에서는 영상 해상도 개선을 위한 고속 다중 혼합영상 보간법을 제안한다. 제안하는 방법은 입력 영상의 4개의 부영상으로부터 12개의 예상되는 부족분을 추정하고, 추정된 부족분과 입력 영상을 결합한 후 보간 함수를 거쳐서 결과 영상을 생성한다. 제안하는 방법은 비교 방법들보다 PSNR에서 최대 1.9dB, SSIM에서 최대 0.052 개선된 결과를 나타내었으며, 주관적 화질 비교에서도 우위에 있음을 실험을 통해서 알 수 있었다. 알고리즘의 동작속도 비교를 통해서 기존의 방법들보다 최소 3배 이상 빠르게 동작하는 것을 알 수 있었다. 제안하는 방법은 영상 해상도 개선을 위한 응용 환경에서 유용하게 사용될 수 있다.

• Journal of Mechanical Science and Technology
• /
• 제17권3호
• /
• pp.457-466
• /
• 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.

• International Journal of Precision Engineering and Manufacturing
• /
• 제3권1호
• /
• pp.33-42
• /
• 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 .