2024/09/08 by Ariana N. Brown, Julianne Chung, Brown, Ariana N. +5 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #15A29 #65F10 #65F22 #65K10 #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2409.05239
openalex publication_date 2024/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this study, we introduce two new Krylov subspace methods for solving rectangular large-scale linear inverse problems. The first approach is a modification of the Hessenberg iterative algorithm that is based off an LU factorization and is therefore referred to as the least squares LU (LSLU) method. The second approach incorporates Tikhonov regularization in an efficient manner; we call this the Hybrid LSLU method. Both methods are inner-product free, making them advantageous for high performance computing and mixed precision arithmetic. Theoretical findings and numerical results show that Hybrid LSLU can be effective in solving large-scale inverse problems and has comparable performance with existing iterative projection methods.