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A recursive algorithm for the inverse factorization S^-1 = ZZ* of Hermitian positive definite matrices S is proposed. Iterative refinement [A.M.N. Niklasson, Phys. Rev. Lett. 70, 193102 (2004)] is combined with a recursive decomposition of S. It is proved that the recursive algorithm always converges if a binary principal submatrix tree is used for the recursive decomposition. As the algorithm uses only matrix--matrix multiplication it can be parallelized and the computational effort increases linearly with system size for sufficiently sparse matrices. Host: A.M.N. Niklasson |