Fast spherical harmonic analysis: A quick algorithm for generating and/or inverting full-sky, high-resolution cosmic microwave background anisotropy maps

We present a fast algorithm for generating full-sky, high-resolution (similar to 5') simulations of the cosmic microwave background anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of a(im) values and the spectral coefficients C-l. We show that using an equidistant cylindrical projection of the sky substantially speeds up the calculations. Thus, generating and/or inverting a full-sky, high-resolution map can be easily achieved with present-day computer technology.