27th Conference of the International Linear Algebra Society (ILAS 2026)

Multigrid-Accelerated Sparsity-Promoting Projection Methods for Inverse Problems

May 22, 2026, 8:45 AM

25m

Torgersen Hall 1030 (Virginia Tech)

Minisymposium Talk Inverse Problems and Uncertainty Quantification through the Lens of Numerical Linear Algebra Inverse Problems and Uncertainty Quantification through the Lens of Numerical Linear Algebra

Speaker

Jonathan Lindbloom (Dartmouth College)

Description

Hybrid projection methods are an effective iterative approach for the solution of large-scale linear inverse problems, including those promoting sparsity in the recovered solution. Priorconditioned (prior-preconditioned) hybrid methods have been proposed to improve performance, but introduce additional computational costs in each iteration related to the application of a weighted pseudoinverse to a matrix of basis vectors. We propose to use multigrid-preconditioned block Krylov methods to accelerate the application of the weighted pseudoinverses in each iteration, which are suitable for both distributed CPU and GPU computing environments. Numerical results are presented for large-scale static and dynamic inverse problems.