Calculating the Inverse Matrix After Some Elements in the Matrix Change

In the current paper two research issues are addressed. First, a new efficient computational formula is presented that can calculate the inverse of a matrix when two elements are perturbed. The formula extends the result of G. Zielke. Second, a fast algorithm for computing an element in an inverse matrix has been derived. This algorithm is very practical in real-world scenarios. Interesting numerical examples demonstrate the feasibility of these algorithms.