2024/09/12 by James G. Nagy, Nagy, James G., Lucas Onisk +1 · 1 citation
Mathematics · #5A29 65F10 65F22 65F08 #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2409.08335
openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This study investigates the iterative refinement method applied to the solution of linear discrete inverse problems by considering its application to the Tikhonov problem in mixed precision. Previous works on mixed precision iterative refinement methods for the solution of symmetric positive definite linear systems and least-squares problems have shown regularization to be a key requirement when computing low precision factorizations. For problems that are naturally severely ill-posed, we formulate the iterates of iterative refinement in mixed precision as a filtered solution using the preconditioned Landweber method with a Tikhonov-type preconditioner. Through numerical examples simulating various mixed precision choices, we showcase the filtering properties of the method and the achievement of comparable working accuracy of discrete inverse problems (i.e., to within a few decimal places in relative error) compared to results computed in double precision as well as another approximate iterative refinement method which we use as a benchmark.