  Two accelerated imaginary-time evolution methods are proposed for the
computation of solitary waves in arbitrary spatial dimensions. For the first
method (with traditional power normalization), the convergence conditions as
well as conditions for optimal accelerations are derived. In addition, it is
shown that for nodeless solitary waves, this method converges if and only if
the solitary wave is linearly stable. The second method is similar to the first
method except that it uses a novel amplitude normalization. The performance of
these methods is illustrated on various examples. It is found that while the
first method is competitive with the Petviashvili method, the second method
delivers much better performance than the first method and the Petviashvili
method.
