• Title/Summary/Keyword: Schur decomposition

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A Study on The eigen-properties on Varied Structural 2-Dim. Waveguides by Krylov-Schur Iteration Method (Krylov-Schur 순환법을 이용한 다양한 2차원 구조의 도파관들에 관한 연구)

  • Kim, Yeong Min;Lim, Jong Soo
    • Journal of the Institute of Electronics and Information Engineers
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    • v.51 no.2
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    • pp.10-14
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    • 2014
  • Krylov-Schur iteration method has been applied to the 2-Dim. waveguides of the varied geometrical structure. The eigen-equations for them have been constructed from FEM based on the tangential edge vectors of triangular elements. The eigen-values and their modes have been determined from the diagonal components of the Schur matrices and its transforming matrices. The eigen-pairs as the results have been revealed visually in the schematic representations.

Legendre Tau Method for the 2-D Stokes Problem

  • Jun, SeRan;Kang, Sungkwon;Kwon, YongHoon
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.2
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    • pp.111-133
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    • 2000
  • A Legendre spectral tau approximation scheme for solving the two-dimensional stationary incompressible Stokes equations is considered. Based on the vorticity-stream function formulation and variational forms, boundary value and normal derivative of vorticity are computed. A factorization technique for matrix stems based on the Schur decomposition is derived. Several numerical experiments are performed.

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A Study on Eigen-properties of a 3-Dim. Resonant Cavity by Krylov-Schur Iteration Method (Krylov-Schur 순환법을 이용한 3-차원 원통구조 도파관의 고유특성 연구)

  • Kim, Yeong Min;Lim, Jong Soo
    • Journal of the Institute of Electronics and Information Engineers
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    • v.51 no.7
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    • pp.142-148
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    • 2014
  • Krylov-Schur iteration method has been applied to the 3-Dim. resonant cavity of a cylindrical form. The vector Helmholtz equation has been analysed for the resonant field strength in homogeneous media by FEM. An eigen-equation has been constructed from element equations basing on tangential edges of the tetrahedra element. This equation made up of two square matrices associated with the curl-curl form of the Helmholtz operator. By performing Krylov-Schur iteration loops on them, Eigen-values and their modes have been determined from the diagonal components of the Schur matrices and its transforming matrices. Eigen-pairs as a result have been revealed visually in the schematic representations. The spectra have been compared with each other to identify the effect of boundary conditions.

A Study On The Eigen-properties of A 2-D Square Waveguide by the Krylov-Schur Iteration Method (Krylov-Schur 순환법에 의한 2차원 사각도파관에서의 고유치 문제에 관한 연구)

  • Kim, Yeong Min;Kim, Dongchool;Lim, Jong Soo
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.11
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    • pp.28-35
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    • 2013
  • The Krylov-Schur algorithm has been applied to reveal the eigen-properties of the wave guide having the square cross section. The eigen-matrix equation has been constructed from FEM with the basis function of the tangential edge-vectors of the triangular element. This equation has been treated firstly with Arnoldi decomposition to obtain a upper Hessenberg matrix. The QR algorithm has been carried out to transform it into Schur form. The several eigen values satisfying the convergent condition have appeared in the diagonal components. The eigen-modes for them have been calculated from the inverse iteration method. The wanted eigen-pairs have been reordered in the leading principle sub-matrix of the Schur matrix. This sub-matrix has been deflated from the eigen-matrix equation for the subsequent search of other eigen-pairs. These processes have been conducted several times repeatedly. As a result, a few primary eigen-pairs of TE and TM modes have been obtained with sufficient reliability.

DECOMPOSITION OF SOME CENTRAL SEPARABLE ALGEBRAS

  • Park, Eun-Mi;Lee, Hei-Sook
    • Journal of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.77-85
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    • 2001
  • If an Azumaya algebra A is a homomorphic image of a finite group ring RG where G is a direct product of subgroups then A can be decomposed into subalgebras A(sub)i which are homomorphic images of subgroup rings of RG. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that A is represented by Azumaya group ring RG, we study relationships between the representing groups for A and A(sub)i.

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2D Finite Difference Time Domain Method Using the Domain Decomposition Method (영역분할법을 이용한 2차원 유한차분 시간영역법 해석)

  • Hong, Ic-Pyo
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.17 no.5
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    • pp.1049-1054
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    • 2013
  • In this paper, two-dimensional(2-D) Finite Difference Time Domain(FDTD) method using the domain decomposition method is proposed. We calculated the electromagnetic scattering field of a two dimensional rectangular Perfect Electric Conductor(PEC) structure using the 2-D FDTD method with Schur complement method as a domain decomposition method. Four domain decomposition and eight domain decomposition are applied for the analysis of the proposed structure. To validate the simulation results, the general 2-D FDTD algorithm for the total domain are applied to the same structure and the results show good agreement with the 2-D FDTD using the domain decomposition method.

CAUCHY DECOMPOSITION FORMULAS FOR SCHUR MODULES

  • Ko, Hyoung J.
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.41-55
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    • 1992
  • The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

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Reliable $H_\infty$ control for descriptor systems with actuator failures (구동기 고장을 가지는 특이시스템의 신뢰 $H_\infty$ 제어)

  • Kim, Jong-Hae
    • Proceedings of the KIEE Conference
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    • 2003.11b
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    • pp.135-138
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    • 2003
  • In this paper, we provide a reliable few controller design method for descriptor systems satisfying asymptotic stability with $H_\infty$ norm bound and all actuator failures occurred within the pre-specified subset. The proper condition for the existence of a reliable $H_\infty$ controller and the controller design method are proposed by linear matrix inequality(LMI), Schur complements, and singular value decomposition. All solutions can be obtained simultaneously because the presented sufficient condition can be expressed as an LMI form.

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Guaranteed cost control for singular systems with time delays using LMI

  • Kim, Jong-Hae
    • 제어로봇시스템학회:학술대회논문집
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    • 2002.10a
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    • pp.44.1-44
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    • 2002
  • This paper is concerned with the problem of designing a guaranteed cost state feedback controller for singular systems with time-varying delays. The sufficient condition for the existence of a guaranteed cost controller, the controller design method, and the optimization problem to get the upper bound of guaranteed cost function are proposed by LMI(linear matrix inequality), singular value decomposition, Schur complements, and change of variables. Since the obtained sufficient conditions can be changed to LMI form, all solutions including controller gain and upper bound of guaranteed cost function can be obtained simultaneously.

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A DIRECT SOLVER FOR THE LEGENDRE TAU APPROXIMATION FOR THE TWO-DIMENSIONAL POISSON PROBLEM

  • Jun, Se-Ran;Kang, Sung-Kwon;Kwon, Yong-Hoon
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.25-42
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    • 2007
  • A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem is proposed. Using the factorization of symmetric eigenvalue problem, the algorithm overcomes the weak points of the Schur decomposition and the conventional diagonalization techniques for the Legendre tau approximation. The convergence of the method is proved and numerical results are presented.