• Title/Summary/Keyword: s-matrix

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CONVERGENCE OF NEWTON'S METHOD FOR SOLVING A CLASS OF QUADRATIC MATRIX EQUATIONS

  • Kim, Hyun-Min
    • Honam Mathematical Journal
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    • v.30 no.2
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    • pp.399-409
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    • 2008
  • We consider the most generalized quadratic matrix equation, Q(X) = $A_7XA_6XA_5+A_4XA_3+A_2XA_1+A_0=0$, where X is m ${\times}$ n, $A_7$, $A_4$ and $A_2$ are p ${\times}$ m, $A_6$ is n ${\times}$ m, $A_5$, $A_3$ and $A_l$ are n ${\times}$ q and $A_0$ is p ${\times}$ q matrices with complex elements. The convergence of Newton's method for solving some different types of quadratic matrix equations are considered and we show that the elementwise minimal positive solvents can be found by Newton's method with the zero starting matrices. We finally give numerical results.

LEAST SQUARES SOLUTIONS OF THE MATRIX EQUATION AXB = D OVER GENERALIZED REFLEXIVE X

  • Yuan, Yongxin
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.471-479
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    • 2008
  • Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.

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SOLVING MATRIX POLYNOMIALS BY NEWTON'S METHOD WITH EXACT LINE SEARCHES

  • Seo, Jong-Hyeon;Kim, Hyun-Min
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.2
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    • pp.55-68
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    • 2008
  • One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form $P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m$, where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ complex matrices. Newton's method was introduced a useful tool for solving the equation P(X)=0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.

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SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES

  • Miladinovic, Marko;Stanimirovic, Predrag
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.33-48
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    • 2011
  • The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.

A HYBRID SCHEME USING LU DECOMPOSITION AND PROJECTION MATRIX FOR DYNAMIC ANALYSIS OF CONSTRAINED MULTIBODY SYSTEMS

  • Yoo, W.S.;Kim, S.H.;Kim, O.J.
    • International Journal of Automotive Technology
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    • v.2 no.3
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    • pp.117-122
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    • 2001
  • For a dynamic analysis of a constrained multibody system, it is necessary to have a routine for satisfying kinematic constraints. LU decomposition scheme, which is used to divide coordinates into dependent and independent coordinates, is efficient but has great difficulty near the singular configuration. Other method such as the projection matrix, which is more stable near a singular configuration, takes longer simulation time due to the large amount of calculation for decomposition. In this paper, the row space and the null space of the Jacobian matrix are proposed by using the pseudo-inverse method and the projection matrix. The equations of the motion of a system are replaced with independent acceleration components using the null space of the Jacobian matrix. Also a new hybrid method is proposed, combining the LU decomposition and the projection matrix. The proposed hybrid method has following advantages. (1) The simulation efficiency is preserved by the LU method during the simulation. (2) The accuracy of the solution is also achieved by the projection method near the singular configuration.

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On Fast M-Gold Hadamard Sequence Transform (고속 M-Gold-Hadamard 시퀀스 트랜스폼)

  • Lee, Mi-Sung;Lee, Moon-Ho;Park, Ju-Yong
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.47 no.7
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    • pp.93-101
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    • 2010
  • In this paper we generate Gold-sequence by using M-sequence which is made by two primitive polynomial of GF(2). Generally M-sequence is generated by linear feedback shift register code generator. Here we show that this matrix of appropriate permutation has Hadamard matrix property. This matrix proves that Gold-sequence through two M-sequence and additive matrix of one column has one of major properties of Hadamard matrix, orthogonal. and this matrix show another property that multiplication with one matrix and transpose matrix of this matrix have the result of unit matrix. Also M-sequence which is made by linear feedback shift register gets Hadamard matrix property mentioned above by adding matrices of one column and one row. And high-speed conversion is possible through L-matrix and the S-matrix.

GENERALIZED EULER PROCESS FOR SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS

  • Yu, Dong-Won
    • Journal of applied mathematics & informatics
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    • v.7 no.3
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    • pp.941-958
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    • 2000
  • Euler method is generalized to solve the system of nonlinear differential equations. The generalization is carried out by taking a special constant matrix S so that exp(tS) can be exactly computed. Such a matrix S is extracted from the Jacobian matrix of the given problem. Stability of the generalized Euler process is discussed. It is shown that the generalized Euler process is comparable to the fourth order Runge-Kutta method. We also exemplify that the important qualitative and geometric features of the underlying dynamical system can be recovered by the generalized Euler process.

ON DIFFERENTIABILITY OF THE MATRIX TRACE OPERATOR AND ITS APPLICATIONS

  • Dulov, E.V.;Andrianova, N.A.
    • Journal of applied mathematics & informatics
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    • v.8 no.1
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    • pp.97-109
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    • 2001
  • This article is devoted to “forgotten” and rarely used technique of matrix analysis, introduced in 60-70th and enhanced by authors. We will study the matrix trace operator and it’s differentiability. This idea generalizes the notion of scalar derivative for matrix computations. The list of the most common derivatives is given at the end of the article. Additionally we point out a close connection of this technique with a least square problem in it’s classical and generalized case.

Polynomial matrix decomposition in the digital domain and its application to MIMO LBR realizations (디지탈 영역에서의 다항식 행렬의 분해와 MIMO LBR 구현에의 응용)

  • 맹승주;임일택;이병기
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.34S no.1
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    • pp.115-123
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    • 1997
  • In this paper we present a polynomial matrix decomposition algorithm that determines a polynomial matix M(z) which satisfies the relation V(z)=M(z) for a given polynomial matrix V(z) which is paraconjugate hermitian matrix with normal rank r and is positive semidenfinite on the unit circle of z-plane. All the decomposition procedures in this proposed method are performed in the digitral domain. We also discuss how to apply the polynomial matirx decomposition in realizing MIMO LBR two-pairs.

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Direct Calculation of A Matrix in Multimachine Electric Power Systems (다수 발전기 계통의 A행렬 직접계산법)

  • Kwon, Sae-Hyuk
    • Proceedings of the KIEE Conference
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    • 1989.07a
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    • pp.221-225
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    • 1989
  • Direct calculation algorithm for the elements of A matrix in multimachine power systems with constant impedance loads has been suggested. Generator's rotor parameters need not be determined from the manufacturer's data. We can identify the elements of A matrix into two categories: One is related to only generator parameters, and the other is related to generator parameters, initial values, and $Z_{Bus}$ matrix.

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