MAPCUMBA: A fast iterative multi-grid map-making algorithm for CMB experiments

The data analysis of current Cosmic Microwave Background (CMB) experiments like BOOMERanG or MAXIMA poses severe challenges which already stretch the limits of current (super-) computer capabilities, if brute force methods are used. In this paper we present a practical solution for the optimal map making problem which can be used directly for next generation CMB experiments like ARCHEOPS and TopHat, and can probably be extended relatively easily to the full PLANCK case. This solution is based on an iterative multi-grid Jacobi algorithm which is both fast and memory sparing. Indeed, if there are N_tod data points along the one dimensional timeline to analyse, the number of operations is of O (N_tod \ln N_tod) and the memory requirement is O (N_tod). Timing and accuracy issues have been analysed on simulated ARCHEOPS and TopHat data, and we discuss as well the issue of the joint evaluation of the signal and noise statistical properties.