Distributed iterate-collapse inversion (DICI) algorithm for L-banded matrices

In this paper, we present a distributed algorithm to invert L-banded matrices that are symmetric positive definite (SPD), when the sub-matrices in the band are distributed among several processing nodes. We provide a distributed iterate-collapse inversion (DICI) algorithm that converges, at each node, to the corresponding submatrices in the inverse of the L-banded matrix. The computational complexity of the DICI algorithm to invert an SPD L-banded n x n matrix can be shown at each node to be independent of the size, n, of the matrix. Local information exchange is carried out after each iteration to guarantee convergence. We apply this algorithm to invert the information matrices in a computationally efficient distributed implementation of the Kalman filter and show its application towards inverting arbitrary sparse SPD matrices.