A note on the convergence of multigrid methods for the Riesz-space equation and an application to image deblurring
arxiv(2024)
摘要
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.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要