Kaczmarz Algorithm and Frames
arXiv:1409.8310
Abstract
Sequences of unit vectors for which the Kaczmarz algorithm always converges in Hilbert space can be characterized in frame theory by tight frames with constant 1. We generalize this result to the context of frames and bases. In particular, we show that the only effective sequences which are Riesz bases are orthonormal bases. Moreover, we consider the infinite system of linear algebraic equations and characterize the (bounded) matrices for which the Kaczmarz algorithm always converges to a solution.
arXiv commentInternational Journal of Wavelets, Multiresolution and Information Processing, Vol. 11, no. 05, 2013