A Matrix Inverse Algorithm based on Bi-Directional Graph Search

We present an algorithm to estimate a single entry of the inverse of a matrix; it is derived using a bidirectional search on a flow graph. This method has immediate application in analyzing dynamical system destabilization attacks, where previous research quantifies system node-to-node vulnerability in terms of a matrix inverse. We present evidence that the expected $\infty$-norm error, the number of floating point operations, and the number of unique entries used to complete the computation are comparable to existing row or column approximation methods.