A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS 𝐿2 spaces
Advances in Operator Theory
Mathematics & Statistics
We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as “the” Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral theory of operators in Hilbert space, to optimization, to large sparse systems, to iterated function systems (IFS), and to fractal harmonic analysis. We present a new recursive iteration scheme involving as input a prescribed sequence of selfadjoint projections. Applications include random Kaczmarz recursions, their limits, and their error-estimates.
Song, Myung-Sin; Jorgensen, Palle; and Tian, James, "A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS 𝐿2 spaces" (2020). SIUE Faculty Research, Scholarship, and Creative Activity. 112.