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Efficient Inversion of Large Overlapped Block Diagonal Matrices

Dinis, R. ; Silva, J. C. ; Souto, N.S.

Efficient Inversion of Large Overlapped Block Diagonal Matrices, Proc ITC-CSCC, Seoul, Korea, South, Vol. 1, pp. 5 - 8, June, 2015.

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The optimum separation of multiple users in cellular systems with universal frequency reuse involves inverting matrices large matrices where all elements are zero (or close to it), with the exception of the main diagonal, as well as a few elements in adjacent diagonals. One of those matrices is an overlapped block diagonal matrix, which is made of many small square matrices along the main diagonal that partially overlap.
In this paper we propose an efficient method for inverting this type of matrices. Our approach takes into account the zero elements of the matrices (optimized algorithms), and allows gains of 30% of the number of operations by using an optimized Cholesky algorithm, compared to an optimized Gauss algorithm.