3 papers
math.NA2021
Optimal Convergence of the Discrepancy Principle for polynomially and exponentially ill-posed Operators under White Noise
Tim Jahn
We consider a linear ill-posed equation in the Hilbert space setting under white noise. Known convergence results for the discrepancy principle are either restricted to Hilbert-Sch…
math.NA2020
On the Discrepancy Principle for Stochastic Gradient Descent
Tim Jahn, Bangti Jin
Stochastic gradient descent (SGD) is a promising numerical method for solving large-scale inverse problems. However, its theoretical properties remain largely underexplored in the…
math.NA2018
Beyond the Bakushinskii veto: Regularising linear inverse problems without knowing the noise distribution
Bastian Harrach, Tim Jahn, Roland Potthast
This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinski…