The paper presents an efficient formula and algorithm for calculating inverse matrix elements after perturbation, indicating practical application potential.
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.
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Zheng et al. (2026) studied this question.
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