충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권2호
  • /
  • Pages.275-285
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  • 2013
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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SKEW-SYMMETRIC SOLVENT FOR SOLVING A POLYNOMIAL EIGENVALUE PROBLEM

  • Han, Yin-Huan (School of Mathematics and Physics Qingdao University of Science and Technology) ;
  • Kim, Hyun-Min (Department of Mathematics Pusan National University)
  • 투고 : 2012.10.11
  • 심사 : 2013.04.04
  • 발행 : 2013.05.15
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초록

In this paper a nonlinear matrix equation is considered which has the form $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_{m-1}X+A_m=0$$ where X is an $n{\times}n$ unknown real matrix and $A_m$, $A_{m-1}$, ${\cdots}$, $A_0$ are $n{\times}n$ matrices with real elements. Newtons method is applied to find the skew-symmetric solvent of the matrix polynomial P(X). We also suggest an algorithm which converges the skew-symmetric solvent even if the Fr$\acute{e}$echet derivative of P(X) is singular.

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참고문헌

  1. Y. Han and H. Kim, Finding the skew-symmetric solvent to a quadratic matrix euqation, To appear in East Asian Math. Jour.
  2. N. J. Higham and H. Kim, Numerical Analysis of a Quadratic Matrix Equation, IMA J. Numer. Anal. 20 (2000), 499-519. https://doi.org/10.1093/imanum/20.4.499
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  4. N. J. Higham and H. Kim, Numerical Analysis of a Quadratic Matrix Equation, IMA J. Numer. Anal. 20 (2000), 499-519. https://doi.org/10.1093/imanum/20.4.499
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