TY  - BOOK
AU  - Md Sarowar Morshed
TI  - Stochastic Steepest Descent Methods for Linear Systems: Greedy Sampling & Momentum
PY  - 2020///
PB  - arXiv
N1  - Open access — freely available to read
N2  - Recently proposed adaptive Sketch & Project (SP) methods connect several well-known projection methods such as Randomized Kaczmarz (RK), Randomized Block Kaczmarz (RBK), Motzkin Relaxation (MR), Randomized Coordinate Descent (RCD), Capped Coordinate Descent (CCD), etc. into one framework for solving linear systems. In this work, we first propose a Stochastic Steepest Descent (SSD) framework that connects SP methods with the well-known Steepest Descent (SD) method for solving positive-definite linear system of equations. We then introduce two greedy sampling strategies in the SSD framework that allow us to obtain algorithms such as Sampling Kaczmarz Motzkin (SKM), Sampling Block Kaczmarz (SBK), Sampling Coordinate Descent (SCD), etc. In doing so, we generalize the existing sampling rules into one framework and develop an efficient version of SP methods. Furthermore, we incorporated the Po
UR  - https://arxiv.org/pdf/2012.13087v1
ER  -