• 제목/요약/키워드: Generalized Inverse

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SOME DECOMPOSITION FORMULAS ASSOCIATED WITH THE SARAN FUNCTION FE

  • Kim, Yong-Sup;Hasanov, Anvar;Lee, Chang-Hyun
    • 호남수학학술지
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    • 제32권4호
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    • pp.581-592
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    • 2010
  • With the help of some techniques based upon certain inverse pairs of symbolic operators initiated by Burchnall-Chaundy, the authors investigate decomposition formulas associated with Saran's function $F_E$ in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By employing their decomposition formulas, we also present a new group of integral representations for the Saran function $F_E$.

잰킷 행렬을 이용한 저밀도 부호의 구성 (Low Density Codes Construction using Jacket Matrices)

  • 문명룡;이광재;;황기연;이문호
    • 대한전자공학회논문지TC
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    • 제42권8호
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    • pp.1-10
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    • 2005
  • 본 논문에서는 대수 이론과 관련된 일반화된 치환 행렬로부터 저밀도 부호의 명시적 구성을 고찰하였으며, 순환공식과 치환행렬에 관한 재킷 역 블록 행렬을 설계하였다. 설계 결과로부터 제안 기법은 저밀도 부호를 얻기 위한 간단하며, 고속화된 기법임을 알 수 있다. 또한, $\pi$-회전 LDPC(low density parity check) 부호와 같은 구조화 LDPC 부호 역시 저밀도 재킷 역 블록 행렬임을 증명하였다.

선형 모형에서 모수 추정을 위한 일반화 역행렬 및 SAS IML 이론에 관한 연구 (G-Inverse and SAS IML for Parameter Estimation in General Linear Model)

  • 최규정;강관중;박병전
    • 응용통계연구
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    • 제20권2호
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    • pp.373-385
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    • 2007
  • 선형모형에서 최소자승법에 의한 정규방정식의 해는 유일하지 않은 경우도 있는데 문헌에 따르면 일반화 역행렬을 정의하여, 그 해를 SAS IML로 취급하고 있다. 본 논문에서는 이것에 대한 이론을 보다 체계화하여 교육 및 연구에 도움을 주고자 하는데 그 목적이 있다.

RANKS OF SUBMATRICES IN A GENERAL SOLUTION TO A QUATERNION SYSTEM WITH APPLICATIONS

  • Zhang, Hua-Sheng;Wang, Qing-Wen
    • 대한수학회보
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    • 제48권5호
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    • pp.969-990
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    • 2011
  • Assume that X, partitioned into $2{\times}2$ block form, is a solution of the system of quaternion matrix equations $A_1XB_1$ = $C_1,A_2XB_2=C_2$. We in this paper give the maximal and minimal ranks of the submatrices in X, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. As applications, we consider the common inner inverse G, partitioned into $2{\times}2$ block form, of two quaternion matrices M and N. We present the formulas of the maximal and minimal ranks of the submatrices of G, and describe the properties of the submatrices of G as well. The findings of this paper generalize some known results in the literature.

5축 CNC 공작기계의 오차합성모델링 및 보정 알고리즘 (Error Synthesis Modeling and Compensation Algorithm of a 5-Axis CNC Machine Tool)

  • 양승한;이철수
    • 한국정밀공학회지
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    • 제16권8호
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    • pp.122-129
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    • 1999
  • A 5-axis CNC machine tool is more useful compared with a 3-axis machine tool, because the position and the orientation of a tool tip can be controlled simultaneously. Unlike the 3-axis machine tool, the 5-axis machine tool has the volumetric position error and volumetric orientation error due to the quasi-static error of each machine tool joint which is a major source of machined part error. So, the generalized error synthesis model of the 5-axis CNC machine tool was developed to predict and to compensate for the volumetric position error and the volumetric orientation error. It was proposed that a compensation algorithm to correct simultaneously the volumetric position error and the volumetric orientation error of the 5-axis CNC machine by error inverse kinematic.

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변위제약모드를 갖는 트러스구조물의 형태해석에 관한 연구 (A Study on the Shape Analysis of the Truss Structures under the Prescribed Displacement Mode)

  • 문창훈;김진기;최옥훈;한상을
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 1997년도 가을 학술발표회 논문집
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    • pp.262-269
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    • 1997
  • The purpose of this study is to survey the shape finding of the plane truss structures under the prescribed displacement mode by the shape analysis. The shape analysis is peformed by the existence condition of a solution and Moore-Penrose generalized inverse matrix, and the prescribed displacement mode is the homologous deformation of structures. The shape analysis of structures is a kind of inverse problem and become the problem of a nonlinear equation. Newton-Raphson method is used to improve the accuracy of approximated solution. To prove the accuracy and the effectiveness of this method, four different shape examples are analyzed.

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DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • 충청수학회지
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    • 제24권4호
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    • pp.745-758
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    • 2011
  • Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.

Parameter estimation of four-parameter viscoelastic Burger model by inverse analysis: case studies of four oil-refineries

  • Dey, Arindam;Basudhar, Prabir Kr.
    • Interaction and multiscale mechanics
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    • 제5권3호
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    • pp.211-228
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    • 2012
  • This paper reports the development of a generalized inverse analysis formulation for the parameter estimation of four-parameter Burger model. The analysis is carried out by formulating the problem as a mathematical programming formulation in terms of identification of the design vector, the objective function and the design constraints. Thereafter, the formulated constrained nonlinear multivariable problem is solved with the aid of fmincon: an in-built constrained optimization solver module available in MatLab. In order to gain experience, a synthetic case-study is considered wherein key issues such as the determination and setting up of variable bounds, global optimality of the solution and minimum number of data-points required for prediction of parameters is addressed. The results reveal that the developed technique is quite efficient in predicting the model parameters. The best result is obtained when the design variables are subjected to a lower bound without any upper bound. Global optimality of the solution is achieved using the developed technique. A minimum of 4-5 randomly selected data-points are required to achieve the optimal solution. The above technique has also been adopted for real-time settlement of four oil refineries with encouraging results.

충돌각 제어 호밍유도법칙의 역최적 문제 (Inverse Optimal Problem for Homing Guidance with Angular Constraint)

  • 이진익;이용인
    • 한국항공우주학회지
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    • 제35권5호
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    • pp.412-418
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    • 2007
  • 본 논문에서는 충돌각 구속조건을 갖는 비행체 호밍 제어 유도법칙에 대한 역최적 문제를 제시한다. 편향비례항법 유도법칙의 이득과 LQ 문제에서의 가중치와의 관계를 규명하고, Riccati 방정식으로부터 제어입력이 LQ 최적제어가 되기 위한 영역을 제시한다. 이를 근거로 종말 구속조건을 만족하는 호밍 유도법칙의 제어이득이 최적제어법칙이 되기 위한 범위를 제안한다. 이론적 해석 결과의 타당성은 3-DOF 모의시험을 통하여 확인한다.

AN ITERATIVE METHOD FOR ORTHOGONAL PROJECTIONS OF GENERALIZED INVERSES

  • Srivastava, Shwetabh;Gupta, D.K.
    • Journal of applied mathematics & informatics
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    • 제32권1_2호
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    • pp.61-74
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    • 2014
  • This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.