Randomized Iterative Methods with Alternating Projections
For researchers in numerical linear algebra and optimization, this provides a unified view and new insights into convergence of randomized iterative methods, but is largely a survey/extension of existing work.
The paper unifies sixteen randomized iterative methods (e.g., Kaczmarz, coordinate descent) under a single framework, introduces new schemes, and analyzes convergence via matrix integrals of alternating projectors, with numerical examples demonstrating behavior.
We use a unified framework to summarize sixteen randomized iterative methods including Kaczmarz method, coordinate descent method, etc. Some new iterative schemes are given as well. Some relationships with \textsc{mg} and \textsc{ddm} are also discussed. We analyze the convergence properties of the iterative schemes by using the matrix integrals associated with alternating projectors, and demonstrate the convergence behaviors of the randomized iterative methods by numerical examples.