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

Scalable iterative data-adaptive RKHS regularization for linear inverse problems

May 19, 2026, 3:45 PM

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

Haibo Li (Huazhong University of Science and Technology)

Description

In this talk, I will present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method for solving ill-posed linear inverse problems. This method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive reproducing kernel Hilbert space (RKHS) penalizing the spaces of small singular values. At the core of the method is a new generalized Golub-Kahan bidiagonalization procedure that recursively constructs orthonormal bases for a sequence of RKHS-restricted Krylov subspaces. The method is scalable, with a complexity of O(kmn) for m-by-n matrices, where k denotes the number of iterations. Numerical tests on the Fredholm integral equation and 2D image deblurring demonstrate that it outperforms the widely used L^2 and l^2 norms, consistently producing stable and accurate solutions that converge when the noise level decreases.