A fast banded matrix inversion using connectivity of Schur´s complements

An algorithm for inverting banded matrices which outperforms the existing approaches in terms of arithmetic operation counts is discussed. The algorithm treats the banded matrix as a block tridiagonal matrix and couples the inverse of each block to its neighboring block through the Schur´s complement. Two passes are required through the diagonal blocks to complete the inverse in the banded portion. The overall time complexity of the algorithm is O(n/sup 2/*bw), where n is the size and bw is the bandwidth of the matrix. It is approximately two times faster than the inverse method based on LU decomposition for small bandwidth. The algorithm is especially suited for inverting block tridiagonal matrices and achieves its highest efficiency in this case.<>