Kaczmarz Projection Algorithms in Moving Window: Performance Improvement via Extended Orthogonality & Forgetting

TL;DR

This paper introduces advanced Kaczmarz algorithms with enhanced update and forgetting mechanisms, improving performance by leveraging extended orthogonality and moving window techniques.

Contribution

It presents novel Kaczmarz algorithms incorporating rank two updates, extended orthogonality, and forgetting mechanisms, extending prior rank one update methods.

Findings

Enhanced convergence properties demonstrated

Performance improvements over traditional algorithms

Effective handling of large-scale problems

Abstract

New Kaczmarz algorithms with rank two gain update, extended orthogonality property and forgetting mechanism which includes both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and associated in this report with well-known Kaczmarz algorithms with rank one update.