2024/03/25 by Danyal Ahmad, Marco Donatelli, Ahmad, Danyal +7
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2403.16352
openalex publication_date 2024/03/25 · openalex created_date 2024/03/27 · openalex updated_date 2026/08/04
In the past decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on multigrid methods for a Riesz-space FDE whose theoretical convergence analysis of such multigrids is currently limited to the two-grid method. Here we provide a detailed theoretical convergence study in the case of V-cycle and W-cycle. Moreover, we discuss its use combined with a band approximation and we compare the result with both τ and circulant preconditionings. The numerical tests include 2D problems as well as the extension to the case of a Riesz-FDE with variable coefficients. Finally, we apply the best-performing method to an image deblurring problem with Tikhonov regularization.