The Role of Inexactness in Krylov Subspace Regularization for Inverse Problems
Abstract
Linear discrete inverse problems arise in many areas of science and engineering, from medical imaging and geophysics to atmospheric modelling. Their numerical solution often relies on iterative algorithms, particularly Krylov subspace methods, that can efficiently handle large-scale, ill-posed systems. In many practical settings, however, exact computations of matrix–vector products, preconditioners, or right-hand sides are either infeasible or unnecessary, leading to inexact iterations. This talk explores the interplay between inexactness and the regularizing behaviour of Krylov subspace methods for inverse problems. We discuss how approximate computations influence the regularization effect inherent in early iterations, as well as semiconvergence, and how controlled inexactness may be exploited to improve computational efficiency. The aim is to provide a broad perspective on recent insights and open questions at the interface of inverse problems, iterative solvers, and computational inexactness.
13:00
The Cosmological Grassmannian
Abstract
Are you an academic, researcher, or PhD candidate in Medical Sciences or MPLS aiming to share your research with a global audience? We’re offering two excellent opportunities to learn about writing for The Conversation, publisher of research-based news and analysis worldwide.
Session 1: Introduction to Writing for The Conversation
An online staff briefing on proposals for a temporary congestion charge in Oxford have been arranged with the County Council. This will take place at 11.30am-12.30pm on Monday 30 June. Colleagues interested in the proposals and their potential impact are welcome to join using the Teams links provided.
Following a University-wide communications survey in January 2025, the Internal Communications team is inviting staff to take part in follow-up discussion groups or share their views through a short, anonymous questionnaire during July. The aim is to gather more nuanced feedback that will help shape how the University communicates with staff in the future.