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Journal of the Korean Mathematical Society = 대한수학회지 v.55 no.6, 2018년, pp.1529 - 1540   SCIE
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NEWTON SCHULZ METHOD FOR SOLVING NONLINEAR MATRIX EQUATION Xp + A⁎XA = Q

Kim, Hyun-Min   (Department of Mathematics Pusan National University  ); Kim, Young-jin   (Innovation Center for Industrial Mathematics National Institute for Mathematical Sciences  ); Meng, Jie   (Department of Mathematics Pusan National University  );
  • 초록

    The matrix equation $X^p+A^*XA=Q$ has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix p-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.


  • 주제어

    fixed-point iteration .   Newton's method .   Newton-Schulz algorithm .   local convergence.  

  • 참고문헌 (21)

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