Document Type : Research Paper

Authors

• Negin Bagherpour
• Nezam Mahdavi Amiri

Department of Mathematical Sciences, Sharif University of Technology,

Abstract

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.

Keywords

• Metropolis-Hastings
• steepest-descent algorithm
• conjugate gradient algorithm
• Barzilai-Borwein step length
• inverse approximation