In this talk, we present a few new efficient iteration methods for the computation of solitary waves and their linear-stability spectra for general solitary waves in arbitrary spatial dimensions.On the computation of solitary waves, we present (i) an acceler ated imaginary-time evolution method with amplitude normalization [1]; (ii) a modified squared-operator iteration method [2].We show that method (i) converges faster than the Petviashvili method (when both methods converge), while method (ii) converges for all solitary waves.On the computation of discrete eigenvalues in the linear-stability spectra of solitary waves, we also present two iteration methods:(a) an original-operator iteration method [3]; (b) a modified squared-operator iteration method.