Solving a linear system of equations is needed in many different applications and there exist many different techniques to solve such a system with no need to compute inverse matrix, as a costly and not stable computation. But the challenge is that in some other applications such as 3D prints, the goal is exactly computing the inverse of a matrix. In this paper, an optimization model equivalent to inverse matrix is introduced and an effective algorithm based on steepest-descent and Barzilai-Borwein step length is suggested. We also used conjugate gradient instead, to provide better numerical results. Finally, we used the Metropolis-Hastings algorithm to accelerate the convergence rate. A key point is that even a random step length is working for global convergence. Numerical results look promising based on stability and accuracy.
Bagherpour,N and Mahdavi Amiri,N . (2024). Metropolis-Hasting Idea for Approximating Matrix Inverse. Journal of Algorithms and Computation, 56(2), 151-161. doi: 10.22059/jac.2025.370682.1207
MLA
Bagherpour,N , and Mahdavi Amiri,N . "Metropolis-Hasting Idea for Approximating Matrix Inverse", Journal of Algorithms and Computation, 56, 2, 2024, 151-161. doi: 10.22059/jac.2025.370682.1207
HARVARD
Bagherpour N, Mahdavi Amiri N. (2024). 'Metropolis-Hasting Idea for Approximating Matrix Inverse', Journal of Algorithms and Computation, 56(2), pp. 151-161. doi: 10.22059/jac.2025.370682.1207
CHICAGO
N Bagherpour and N Mahdavi Amiri, "Metropolis-Hasting Idea for Approximating Matrix Inverse," Journal of Algorithms and Computation, 56 2 (2024): 151-161, doi: 10.22059/jac.2025.370682.1207
VANCOUVER
Bagherpour N, Mahdavi Amiri N. Metropolis-Hasting Idea for Approximating Matrix Inverse. J. Algo. Comp.. 2024;56(2):151-161. doi: 10.22059/jac.2025.370682.1207
