近期，我院李海波副教授与合作者的文章《Scalable Iterative Data-Adaptive RKHS Regularization》在国际期刊《SIAM Journal on Scientific Computing》发表。

       摘要：We 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 mby-n matrices, where k denotes the number of iterations. Numerical tests on the Fredholm integral equation and two-dimensional image deblurring demonstrate that it outperforms the widely used L2 and l2 norms, consistently producing stable and accurate solutions that converge when the noise level decreases.

        论文链接：https://epubs.siam.org/doi/10.1137/24M1628104