Abstract
A rich variety of Krylov Subspace methods are extensively used for the solution of linear systems. In particular, the investigation of the convergence of BiCG and CGS methods is a key for devising new iterative methods. In this paper, we clarify the effect of a range of initial shadow residual r^*_0 for BiCG and CGS methods. We propose using r^*_0=(A^T)^mr_0 and r^*_0=(A^T)^m×(random vector), (m=0,1,2,3). Numerical experiments show that this may enhance the convergence of BiCG and CGS methods.
