Abstract In this paper, we introduce a new efficient iterative method to compute the weighted Moore–Penrose inverse of a singular or rectangular real (or complex) matrix, which requires five matrix multiplications per iteration. The proposed method has been shown to be fourth-order convergent to the weighted Moore–Penrose inverse. The average number of iterations, the average total number of matrix multiplications, and the average elapsed execution time of compared methods are computed using ten matrices in each dimension. The numerical results are based on random matrices of sizes m × m and m × (m + 10), where m = 200, 300, 400, 500, 600. Based on this comparison, our new method can be considered as an efficient and fast method with low computational cost to compute the weighted Moore–Penrose inverse.
