Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization

Abstract

The Landweber method is a well-known iterative procedure to compute regularized solutions of linear operator equations in Hilbert spaces. Unfortunately it is also known to be very slow. Likewise its generalization to Banach spaces has good regularizing properties but slow convergence. This article intends to give a short survey about the use of sequential subspace optimization to accelerate this method while preserving its regularizing properties.