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arXiv · 2510.18865

New flexible and inexact Golub-Kahan algorithms for inverse problems

Malena Sabaté Landman·Silvia Gazzola
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Abstract

This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a solution to (re)weighted least squares problems via projection onto adaptively generated subspaces, where the constraint subspaces for the residuals are (formally) equipped with iteration-dependent preconditioners or inexactness. The new solvers offer a flexible and inexact Krylov subspace alternative to other existing Krylov-based approaches for handling general data fidelity functionals, e.g., those expressed in the $p$-norm. Numerical experiments in imaging applications, such as image deblurring and computed tomography, highlight the effectiveness and competitiveness of the proposed methods with respect to other popular methods.

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Malena Sabaté Landman, Silvia Gazzola. 2025-10-21. New flexible and inexact Golub-Kahan algorithms for inverse problems. https://arxiv.org/abs/2510.18865

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