Two Kinds of Nonlinear Matrix Equations and their Corresponding Matrix Sequences

نویسندگان

  • Xiquan Shi
  • Fengshan Liu
  • Frank Gibson
چکیده

We studied the existence and uniqueness of solutions of the following two kinds of nonlinear matrix equations X = Pk−1 l=0 P T l X lPl, and X = Pk−1 l=0 (P T l XPl) αl , and the convergence of the matrix sequences {Xi} recursively defined by Xn+k = Pk−1 l=0 P T l X αl n+lPl, n ≥ 0, and Xn+k = Pk−1 l=0 (P T l Xn+lPl) αl , n ≥ 0, where |αl| ≤ 1 for 0 ≤ l ≤ k − 1 and X0, · · · , Xk−1 are initial positive definite matrices. AMS classification: 40A05; 15A24

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تاریخ انتشار 2003