A fast approximate solution of a large sparse nonlinear system by monotone convergent iterations

Abstract

In this paper we present a numerical technique to accelerate the rate of convergence process which was developed in [1] to solve iteratively a large sparse nonlinear system of equations. In [1] we described a family of Gauss-Seidel-iterations for the solution of large sparse nonlinear systems Fz = 0, where F:Dcz{N−+y{N. Under realistic condition on the mapping F and suitable starting vectors, we constructed in [1] a family of monotone convergent iterations with respect to both sides. In this paper a linear combination of the current lower and upper iterates has been constructed to achieve a fast monotone convergent process for approximating the solution of Fz = 0. Sufficient conditions are derived to ensure monotone convergence with respect to both sides.

Keywords:

• Monotone iteration
• antitone and isotone mapping
• Gauss-Seidel and SOR-Newton iterations
• Jacobian or Hessian matrix
• positive definite matrix

C.R. Categories:

• G.1.3
• G.1.4
• G.1.8