Generalized tridiagonal preconditioners for solving linear systems

The paper presents a type of tridiagonal preconditioners for solving linear system Ax=b with nonsingular M-matrix A, and obtains some important convergent theorems about preconditioned Jacobi and Gauss–Seidel type iterative methods. The main results theoretically prove that the tridiagonal preconditioners cannot only accelerate the convergence of iterations, but also generalize some known results.