An incomplete factorization iterative technique for elliptic equations

Abstract

This paper describes efficient iterative techniques for solving the large sparse symmetric linear systems that arise from application of finite difference approximations to self-adjoint elliptic equations. We use an incomplete factorization technique with the method of D'Yakonov type, generalized conjugate gradient and Chebyshev semi-iterative methods. We compare these methods with numerical examples. Bounds for the 4-norm of the error vector of the Chebyshev semi-iterative method in terms of the spectral radius of the iteration matrix are derived.

Keywords:

• Incomplete factorization
• Chebyshev semi-iterative method
• spectral radius

C.R. Categories:

• G1.2
• G1.5
• G1.8

^∗This work was supported by a grant from the University of Akron and the computations were performed at NASA Lewis Research Center, Cleveland, Ohio while the author was a summer faculty fellow.

^∗This work was supported by a grant from the University of Akron and the computations were performed at NASA Lewis Research Center, Cleveland, Ohio while the author was a summer faculty fellow.

Notes

^∗This work was supported by a grant from the University of Akron and the computations were performed at NASA Lewis Research Center, Cleveland, Ohio while the author was a summer faculty fellow.