Investigating the composite step biconjugate A-orthogonal residual method for non-hermitian linear systems in electromagnetics

An interesting stabilizing variant of the biconjugate A-orthogonal residual (BiCOR) method is investigated for solving non-Hermitian systems of linear equations in electromagnetics. It is naturally based on and inspired by the composite step strategy employed for the composite step biconjugate gradient method. Our motivation is from the point of view of pivot-breakdown treatment when the BiCOR method has erratic convergence behaviors. The present composite step BiCOR method can reduce the number of spikes in the convergence history of the norm of the residuals to the greatest extent. Moreover, it could provide some further practically desired smoothing behavior towards stabilizing the numerical performance of the BiCOR method.