  We present several first-order and second-order numerical schemes for the
Cahn-Hilliard equation with discrete unconditional energy stability. These
schemes stem from the generalized Positive Auxiliary Variable (gPAV) idea, and
require only the solution of linear algebraic systems with a constant
coefficient matrix. More importantly, the computational complexity (operation
count per time step) of these schemes is approximately a half of those of the
gPAV and the scalar auxiliary variable (SAV) methods in previous works. We
investigate the stability properties of the proposed schemes to establish
stability bounds for the field function and the auxiliary variable, and also
provide their error analyses. Numerical experiments are presented to verify the
theoretical analyses and also demonstrate the stability of the schemes at large
time step sizes.
