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There is enormous potential to advance cosmology from statisticalcharacterizations of cosmic microwave background sky maps. The angular powerspectrum of the microwave anisotropy is a particularly important statistic.Existing algorithms for computing the angular power spectrum of a pixelized maptypically require O(N^3) operations and O(N^2) storage, where N is the numberof independent pixels in the map. The MAP and Planck satellites will producemegapixel maps of the cosmic microwave background temperature at multiplefrequencies; thus, existing algorithms are not computationally feasible. Inthis article, we introduce an algorithm that requires O(N^2) operations andO(N^1.5) storage that can find the minimum variance power spectrum from sky mapdata roughly one million times faster than was previously possible. This makesfeasible an analysis that was hitherto intractable.Comment: 35 pages, 8 figures, LaTex, aaspp4. Accepted by ApJ. Minor changes to  match accepted versio

An Efficient Technique to Determine the Power Spectrum from Cosmic Microwave Background Sky Maps