Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	巫文婷特别副研究员，北京理工大学数学与统计学院
Inviter:	白中治研究员
Title:	Randomized Block Kaczmarz Methods
Time & Venue:	2022.10.26 20:00-21:00 腾讯会议：563-304-160
Abstract:	The Kaczmarz method is a classic while effective row-action iteration solver for solving large systems of linear equations. Due to its simplicity, it has been widely used in the area of signal and image processing. Based on the Kaczmarz method, by choosing each row of the coefficient matrix randomly with probability proportional to its squared Euclidean norm, rather than sequentially in the given order, Strohmer and Vershynin constructed the randomized Kaczmarz method for solving consistent linear systems. Zouzias and Freris extended the randomized Kaczmarz method and proposed the randomized extended Kaczmarz method to iteratively compute the least Euclidean norm solution of the linear least-squares problem. In the randomized Kaczmarz method, one row of the coefficient matrix is used in each iterate. In the randomized extended Kaczmarz method, one row and one column of the coefficient matrix are used in each iterate. In this talk, we will discuss some block versions of the randomized Kaczmarz method which utilize more than one row or one column to update the current iterate, including their convergence analysis and numerical performance.