• 제목/요약/키워드: Singular

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ITERATIONS OF THE UNIT SINGULAR INNER FUNCITON

  • Kim, Hong-Oh
    • 대한수학회보
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    • 제25권2호
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    • pp.243-246
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    • 1988
  • Let M(z)=exp (-1+z/1-z) be the unit singular inner function. See [1] or [2] for the basic facts about inner functions. We define the iterations of M9z) as (Fig.) Since the composition M$_{2}$(z)=M.M(z) is known (see [5] for example) to be singular inner function it has the "cannonical" representation (Fig.) where .mu. is a finite, positive singular Borel measure on the unit circle T. In section 2, we have explicit cannonical representation of M$_{2}$(z) by determining the singular measure .mu. In section 3 we show that (Fig.) These facts might have been known but could not be found in the literature.iterature.

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SEMI-CONVERGENCE OF THE PARAMETERIZED INEXACT UZAWA METHOD FOR SINGULAR SADDLE POINT PROBLEMS

  • YUN, JAE HEON
    • 대한수학회보
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    • 제52권5호
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    • pp.1669-1681
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    • 2015
  • In this paper, we provide semi-convergence results of the parameterized inexact Uzawa method with singular preconditioners for solving singular saddle point problems. We also provide numerical experiments to examine the effectiveness of the parameterized inexact Uzawa method with singular preconditioners.

SUFFICIENT CONDITION FOR THE DIFFERENTIABILITY OF THE RIESZ-NÁGY-TAKÁCS SINGULAR FUNCTION

  • Baek, In-Soo
    • 대한수학회보
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    • 제54권4호
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    • pp.1173-1183
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    • 2017
  • We give some sufficient conditions for the null and infinite derivatives of the $Riesz-N{\acute{a}}gy-Tak{\acute{a}}cs$ (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.

On D-admissibility Conditions of Singular Systems

  • Gao, Lixin;Chen, Wenhai
    • International Journal of Control, Automation, and Systems
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    • 제5권1호
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    • pp.86-92
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    • 2007
  • In this paper, we first establish $D_L$-admissibility and $D_R$-admissibility conditions for singular systems. The admissibility conditions expressed as Lyapunov type inequalities extend the existed results of normal systems to singular systems. As special cases the admissibility conditions of the continuous-time and the discrete-time singular systems can be obtained directly. The results established in this paper can be applied to solve the problems of eigenvalue assignment, regional pole-placement and robust control etc.

The Comparison of Singular Value Decomposition and Spectral Decomposition

  • Shin, Yang-Gyu
    • Journal of the Korean Data and Information Science Society
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    • 제18권4호
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    • pp.1135-1143
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    • 2007
  • The singular value decomposition and the spectral decomposition are the useful methods in the area of matrix computation for multivariate techniques such as principal component analysis and multidimensional scaling. These techniques aim to find a simpler geometric structure for the data points. The singular value decomposition and the spectral decomposition are the methods being used in these techniques for this purpose. In this paper, the singular value decomposition and the spectral decomposition are compared.

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특이점 근방에서 역 기구학 해를 구하기 위한 자동 감쇄 분배 방법 (A Damping Distribution Method for Inverse Kinematics Problem Near Singular Configurations)

  • 성영휘
    • 제어로봇시스템학회논문지
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    • 제4권6호
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    • pp.780-785
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    • 1998
  • In this paper, it is shown that the conventional methods for dealing with the singularity problem of a manipulator can be generalized as a local minimization problem with differently weighted objective functions. A new damping method proposed in this article automatically determines the damping amounts for singular values, which are inversely proportional to the magnitude of the singular values. Furthermore, this can be done without explicitly computing the singular values. The proposed method can be applied to all the manipulators with revolute joints.

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Robust Singular Value Decomposition BaLsed on Weighted Least Absolute Deviation Regression

  • Jung, Kang-Mo
    • Communications for Statistical Applications and Methods
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    • 제17권6호
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    • pp.803-810
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    • 2010
  • The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.

A GENERALIZED SINGULAR FUNCTION

  • Baek, In-Soo
    • 충청수학회지
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    • 제23권4호
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    • pp.657-661
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    • 2010
  • We study a singular function which we call a generalized cylinder convex(concave) function induced from different generalized dyadic expansion systems on the unit interval. We show that the generalized cylinder convex(concave)function is a singular function and the length of its graph is 2. Using a local dimension set in the unit interval, we give some characterization of the distribution set using its derivative, which leads to that this singular function is nowhere differentiable in the sense of topological magnitude.

혼합된 감도함수를 이용한 구조적 특이치의 견실성능문제 분석 (Analysis of structured singular value with mixed sensitivity problem in robust performance)

  • 방경호;엄태호;박홍배
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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    • pp.482-485
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    • 1993
  • This paper deals with structured singular value and mixed sensitivity problem for robust performance. We derive the sufficient condition that mixed sensitivity problem satisfies structured singular value in robust performance problem. And we show the bound of perturbation between structured singular value and norm of mixed sensitivity functions.

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