Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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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)
  • Received : 2012.10.11
  • Accepted : 2013.04.04
  • Published : 2013.05.15
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Abstract

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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References

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