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Metropolis-Hasting Idea for Approximating Matrix Inverse | ||
| Journal of Algorithms and Computation | ||
| دوره 56، شماره 2، اسفند 2024، صفحه 151-161 اصل مقاله (1.38 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2025.370682.1207 | ||
| نویسندگان | ||
| Negin Bagherpour* ؛ Nezam Mahdavi Amiri | ||
| Department of Mathematical Sciences, Sharif University of Technology, | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Metropolis-Hastings؛ steepest-descent algorithm؛ conjugate gradient algorithm؛ Barzilai-Borwein step length؛ inverse approximation | ||
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آمار تعداد مشاهده مقاله: 232 تعداد دریافت فایل اصل مقاله: 237 |
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