Kaczmarz Algorithm and Frames
Information Theory
2014-10-01 v1 math.IT
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.
Cite
@article{arxiv.1409.8310,
title = {Kaczmarz Algorithm and Frames},
author = {Wojciech Czaja and James Tanis},
journal= {arXiv preprint arXiv:1409.8310},
year = {2014}
}
Comments
International Journal of Wavelets, Multiresolution and Information Processing, Vol. 11, no. 05, 2013