The Randomized Kaczmarz Method with Application on Making Macroeconomic Predictions

• Main Author: Wan, Dejun
• Format: Others
• Published: Scholarship @ Claremont 2016
• Subjects: Linear Systems; Kaczmarz Method; Macroeconomic Analysis; Numerical Analysis and Computation
• Online Access: http://scholarship.claremont.edu/cmc_theses/1437; http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=2358&context=cmc_theses

This paper will demonstrate the principles and important facts of the randomized Kaczmarz algorithm as well as its extended version proposed by Zouzias and Ferris. Through the analysis made by Strohmer and Vershynin as well as Needell, it can be shown that the randomized Kaczmarz method is theoretically applicable in solving over-determined linear systems with or without noise. The extension of the randomized Kaczmarz algorithm further applies to the linear systems with non-unique solutions. In the experiment section of this paper, we compare the accuracies of the algorithms discussed in the paper in terms of making real-world macroeconomic analyses and predictions. The extended randomized Kaczmarz method outperforms both the randomized Kaczmarz method and the randomized Gauss-Seidel method on our data sets.