We introduce stochastic asymptotical regularization (SAR) methods for the uncertainty
quantification of the stable approximate solution of ill-posed linear-operator equations …

In this work we consider stochastic gradient descent (SGD) for solving linear inverse
problems in Banach spaces. SGD and its variants have been established as one of the most …

Randomized Kaczmarz is a simple iterative method for finding solutions of linear systems
Ax=b. We point out that the arising sequence (x_k)_k=1^∞ tends to converge to the solution …

The Kaczmarz method for solving a linear system $ Ax= b $ interprets such a system as a
collection of equations $\left\langle a_i, x\right\rangle= b_i $, where $ a_i $ is the $ i $-th row …

We study two-layer neural networks whose domain and range are Banach spaces with
separable preduals. In addition, we assume that the image space is equipped with a partial …

In this work, we analyze the regularizing property of the stochastic gradient descent for the
numerical solution of a class of nonlinear ill-posed inverse problems in Hilbert spaces. At …

Consider linear ill-posed problems governed by the system Ai x= yi for i= 1,..., p, where each
Ai is a bounded linear operator from a Banach space X to a Hilbert space Yi. In case p is …

The a posteriori stopping rule plays a significant role in the design of efficient stochastic
algorithms for various tasks in computational mathematics, such as inverse problems …

We provide an overview of recent progress in statistical inverse problems with random
experimental design, covering both linear and nonlinear inverse problems. Different …

Stochastic gradient descent (SGD) is a promising numerical method for solving large-scale
inverse problems. However, its theoretical properties remain largely underexplored in the …