Iterative solution of strongly nonsymmetric systems of linear algebraic equations. (English. Russian original) Zbl 0946.65018

Comput. Math. Math. Phys. 37, No. 11, 1241-1251 (1997); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 11, 1283-1293 (1997).
It is well known that most of the widely accepted preconditioners are designed to improve the properties of the symmetric part of system \(Au=b\). It often happens that difficulties are associated with the ill-conditioned skew-symmetric part of the system to be solved. The preconditioner suggested in this paper allows one to solve the problem in the simplest and most natural way. The authors examine the convergence of Richardson’s method as applied to the preconditioned system in the case when the original matrix is dissipative. Sufficient conditions for the convergence of the method are presented, a procedure for finding the optimal value of the iteration parameter is developed, and an estimate for the convergence rate is given.


65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling