Improving the Truncated Spike Algorithm via Neumann Series Approximations

Large memory overhead of LU decomposition during the factorization stage of the truncated SPIKE algorithm represents a common bottleneck. For large banded diagonally-dominant linear systems, their structure can be leveraged to avoid said LU decompositions. Specifically, Neumann series can be used to approximate these inverse, with smaller memory consumption complexity thus avoiding the excessive growth of the reduced linear system. Convergence of the Neumann series is ensured via a simple scaling of the input matrix. We present results showing the achieved accuracy providing bounds for memory and FLOP count.