A new note on spectra of optimal and superoptimal preconditioned matrices

Recently, Cheng et al. [Lin. Alg. Appl. 422 (2007): 482–485] proposed the spectral comparison of optimal preconditioner in Chan [SIAM J. Sci. Statist. Comput. 9 (1988): 766–771] and superoptimal preconditioner in Tyrtyshnikov [SIAM J. Matrix Anal. Appl. 13 (1992): 459–473]. In this paper, based on the work of Cheng et al., we further compare the spectra of optimal and superoptimal preconditioned matrices.