An iterative algorithm for solving a finite-dimensional linear operator equation T(x)=f with applications

This paper proposes an iterative algorithm for solving a general finite-dimensional linear operator equation T(x)=f and demonstrates that it will get the exact solution within a finite number of iteration steps. This algorithm unifies all the iterative methods in Huang (2008) [3], , Peng (2005) [7], and Peng and Peng (2006) [8] and provides an iterative method for solving an inverse problem related to Hermitian-generalized Hamiltonian matrices [2,12].