Investigating the Composite Step Biconjugate A-Orthogonal Residual Method for Non-Hermitian Dense Linear Systems in Electromagnetics

An interesting stabilizing variant of the biconjugate A-orthogonal residual (BiCOR) method is investigated for solving dense complex non-Hermitian systems of linear equations arising from the Galerlcin discretization of surface integral equations in electromagnetics. The novel variant is naturally based on and inspired by the composite step strategy employed for the composite step biconjugate gradient method from the point of view of pivot-breakdown treatment when the BiCOR method has erratic convergence behaviors. Besides reducing the number of spikes in the convergence history of the norm of the residuals to the greatest extent, the present composite step BiCOR method can provide some further practically desired smoothing behavior towards stabilizing the numerical performance of the BiCOR method in the case of irregular convergence.