On the semigroup property for some structured iterations

Matthew M. Lin, Chun Yueh Chiang

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number112768
JournalJournal of Computational and Applied Mathematics
Volume374
DOIs
Publication statusPublished - 2020 Aug 15

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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