East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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FINDING THE SKEW-SYMMETRIC SOLVENT TO A QUADRATIC MATRIX EQUATION

  • Han, Yin-Huan (School of Mathematics and Physics, Qingdao University of Science and Technology) ;
  • Kim, Hyun-Min (Department of Mathematics, Pusan National University)
  • Received : 2012.09.05
  • Accepted : 2012.09.20
  • Published : 2012.11.30
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Abstract

In this paper we consider the quadratic matrix equation which can be defined be $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix; A,B and C are $n{\times}n$ given matrices with real elements. Newton's method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fr$\acute{e}$chet derivative is singular. Finally, we give some numerical examples.

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References

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