• Title, Summary, Keyword: weighted approximation

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STANCU TYPE GENERALIZATION OF MODIFIED GAMMA OPERATORS BASED ON q-INTEGERS

  • Chen, Shu-Ni;Cheng, Wen-Tao;Zeng, Xiao-Ming
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.359-373
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    • 2017
  • In this paper, we propose the Stancu type generalization of a kind of modified q-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.

On Approximation by Post-Widder and Stancu Operators Preserving x2

  • Rempulska, Lucyna;Skorupka, Mariola
    • Kyungpook Mathematical Journal
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    • v.49 no.1
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    • pp.57-65
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    • 2009
  • In the papers [5]-[7] was examined approximation of functions by the modified Sz$\'{a}$sz-Mrakyan operators and other positive linear operators preserving $e_2(x)=x^2$. In this paper we introduce the Post-Widder and Stancu operators preserving $x^2$ in polynomial weighted spaces. We show that these operators have better approximation properties than classical Post-Widder and Stancu operators.

(Frequency Weighted Reduction Using Iterative Approach of BMI) (BMI의 반복적 해법을 이용한 주파수하중 차수축소)

  • Kim, Yong-Tae;O, Do-Chang;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.39 no.1
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    • pp.33-41
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    • 2002
  • In this paper, we present a frequency weighted model reduction using LMIs for minimizing the H$\infty$ weighted model error compared with the methods of frequency weighted balanced truncation and frequency weighted Hankel norm approximation. The proposed algorithm, its form is equal to the sufficient condition of performance preserving controller approximation, is based on an iterative two-step LMI scheme induced from bound real lemma. So, it can be applied to the problem of the performance preserving controller approximation. The controller reduction is useful in a practical control design and ensures its easy implementation and high reliability The validity of the proposed algorithm is shown through numerical examples. Additionaly, we extend the proposed algorithm to performance preserving controller approximation by applying to the HIMAT(highly maneuverable aircraft technology) system.

APPROXIMATION BY GENUINE LUPAŞ-BETA-STANCU OPERATORS

  • KUMAR, ALOK;VANDANA, VANDANA
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.15-28
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    • 2018
  • In this paper, we introduce a Stancu type generalization of genuine LupaŞ-Beta operators of integral type. We establish some moment estimates and the direct results in terms of classical modulus of continuity, Voronovskaja-type asymptotic theorem, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Lastly, we propose a king type modification of these operators to obtain better estimates.

Distribution of a Sum of Weighted Noncentral Chi-Square Variables

  • Heo, Sun-Yeong;Chang, Duk-Joon
    • Communications for Statistical Applications and Methods
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    • v.13 no.2
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    • pp.429-440
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    • 2006
  • In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

The Performance Evaluation of Missile Warning Radar for GVES (지상기동 장비용 미사일 경고 레이더의 성능 평가)

  • Park, Gyu-Churl;Hong, Sung-Yong
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.20 no.12
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    • pp.1333-1339
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    • 2009
  • A MWR(Missile Warning Radar) of GVES(Ground Vehicle Equipment System) has to effectively decide the threat for a detected target. Linear Approximation Fitting(LAF) and Weighted Linear Approximation Fitting(WLAF) algorithm is proposed as algorithm for a threat decision method. The target is classified into a threat or non-threat using a boundary condition of the angular rate, and the boundary condition is determined using probability model simulation. This paper confirms the performance of proposed threat decision algorithm using measurement.

Improved Element-Free Galerkin method (IEFG) for solving three-dimensional elasticity problems

  • Zhang, Zan;Liew, K.M.
    • Interaction and multiscale mechanics
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    • v.3 no.2
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    • pp.123-143
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    • 2010
  • The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

Szász-Kantorovich Type Operators Based on Charlier Polynomials

  • Kajla, Arun;Agrawal, Purshottam Narain
    • Kyungpook Mathematical Journal
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    • v.56 no.3
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    • pp.877-897
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    • 2016
  • In the present article, we study some approximation properties of the Kantorovich type generalization of $Sz{\acute{a}}sz$ type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.

Krawtchouk Polynomial Approximation for Binomial Convolutions

  • Ha, Hyung-Tae
    • Kyungpook Mathematical Journal
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    • v.57 no.3
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    • pp.493-502
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    • 2017
  • We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

A WEIGHTED GLOBAL GENERALIZED CROSS VALIDATION FOR GL-CGLS REGULARIZATION

  • Chung, Seiyoung;Kwon, SunJoo;Oh, SeYoung
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.1
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    • pp.59-71
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    • 2016
  • To obtain more accurate approximation of the true images in the deblurring problems, the weighted global generalized cross validation(GCV) function to the inverse problem with multiple right-hand sides is suggested as an efficient way to determine the regularization parameter. We analyze the experimental results for many test problems and was able to obtain the globally useful range of the weight when the preconditioned global conjugate gradient linear least squares(Gl-CGLS) method with the weighted global GCV function is applied.