Iterative Refinement and Flexible Iteratively Reweighed Solvers for Linear Inverse Problems with Sparse Solutions
Journal:
arXiv
Published Date:
Feb 4, 2025
Abstract
This paper presents a new algorithmic framework for computing sparse
solutions to large-scale linear discrete ill-posed problems. The approach is
motivated by recent perspectives on iteratively reweighted norm schemes, viewed
through the lens of iterative refinement. This framework leverages the
efficiency and fast convergence of flexible Krylov methods while achieving
higher accuracy through suitable restarts. Additionally, we demonstrate that
the proposed methods outperform other flexible Krylov approaches in
memory-limited scenarios. Relevant convergence theory is discussed, and the
performance of the proposed algorithms is illustrated through a range of
numerical examples, including image deblurring and computed tomography.
