This paper presents, a preconditioned version of global FOM and GMRES methods for solving Lyapunov matrix equations AX + XA = −BTB. These preconditioned methods are based on the global full orthogonalization and generalized minimal residual methods. For constructing effective preconditioners, we will use ADI spiliting of above lyapunov matrix equations. Numerical experiments show that the solut...

Abstract: Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) deals with nonlinear models and/or constraints. A Continuation/GMRESMethod for NMPC, suggested by T. Ohtsuka in 2004, uses the GMRES iterative algorithm to solve a forward difference approximation Ax = b of the original NMPC equations on every time step. We have previousl...

We study the solution of neutral delay differential equations (NDDEs) by using boundary value methods (BVMs). The BVMs require the solution of nonsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed to solve these linear systems. We show that if an Ak1,k2-stable BVM is used for solving an m-by-m system of NDDEs, then our pr...

Two Krylov subspace iterative methods, GMRES and QMR, were studied in conjunction with several preconditioning techniques for solving the linear system raised from the finite element discretisation of incompressible Navier-Stokes equations for hydrodynamic problems. The preconditioning methods under investigation were the incomplete factorisation methods such as ILU(0) and MILU, the Stokes prec...

The purpose of this work is to compare the performance of some preconditioned iterative methods for solving the linear systems of equations, formed at each time-integration step of two-dimensional incompressible NavierStokes equations of fluid flow. The Navier-Stokes equations are discretized in an implicit and upwind control volume formulation. The iterative methods used in this paper include ...

This paper continues the recent work of the authors’ (Numer. Math., to appear) on the rate of convergence of GMRES for a tridiagonal Toeplitz linear system Ax = b. Much simpler formulas than the earlier ones for GMRES residuals when b is the first or the last column of the identity matrix are established, and these formulas allow us to confirm the rate of convergence that was conjectured but on...