A fast method to estimate the Moore-Penrose inverse for well-determined numerical rank matrices based on the Tikhonov regularization

This paper introduces a novel approach for estimating the Moore-Penrose inverse. The method proposed relies on Tikhonov regularization, which requires the computation of all positive singular values of an m × n matrix. Additionally, we present a highly efficient and accurate procedure for estimating these singular values. This procedure assumes the well-determined numerical rank of matrices A^∗A (if m ≥ n) and AA^∗ (if m≤ n). Furthermore, we demonstrate the application of our proposed method in solving linear discrete well-posed problems. The paper concludes with numerical simulations to illustrate the advantages of our novel approach. Notably, we compare the execution time associated with our technique to that of some relevant methods in the existing literature, demonstrating that our method outperforms others in terms of computational efficiency. To further substantiate our findings, we conduct computational experiments to measure execution time and speedup. The results affirm the efficiency of our proposed method, showcasing reduced execution times compared to other methods. This contributes to establishing our approach’s practical viability and effectiveness in diverse applications.