On the semigroup property for some structured iterations

Matthew M. Lin, Chun Yueh Chiang

研究成果: Article同行評審

3 引文 斯高帕斯(Scopus)


Nonlinear matrix equations play a crucial role in science and engineering problems. However, solutions of nonlinear matrix equations cannot, in general, be given analytically. One standard way of solving nonlinear matrix equations is to apply the fixed-point iteration with usually only the linear convergence rate. To advance the existing methods, we exploit in this work one type of semigroup property and use this property to propose a technique for solving the equations with the speed of convergence of any desired order. We realize our way by starting with examples of solving the scalar equations and, also, connect this method with some well-known equations including, but not limited to, the Stein matrix equation, the generalized eigenvalue problem, the generalized nonlinear matrix equation, the discrete-time algebraic Riccati equations to express the capacity of this method.

期刊Journal of Computational and Applied Mathematics
出版狀態Published - 2020 8月 15

All Science Journal Classification (ASJC) codes

  • 計算數學
  • 應用數學


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