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We consider the problem of estimating the inverse of a covariance matrix of a normal distribution, assuming that it is sparse. To this end, an l1 regularized logdeterminant optimization problem is solved. We present a multilevel framework for accelerating existing solvers of this problem. Taking advantage of the sparseness of the matrix, we create a multilevel hierarchy of similar problems, which are traversed in order to accelerate the optimization process. Our numerical experiments demonstrate the efficiency of the multilevel framework for solving both medium and large scale instances of this problem.