000			01421nam a2200169 a 4500
005			20260901030406.0
008			250101s2020 xx o 000 0 eng d
100	1		_aMd Sarowar Morshed
245	1	0	_aStochastic Steepest Descent Methods for Linear Systems: Greedy Sampling & Momentum
264		1	_barXiv _c2020
336			_atext
338			_aonline resource
520			_aRecently 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
506	0		_aOpen access — freely available to read.
856	4	0	_uhttps://arxiv.org/pdf/2012.13087v1 _yRead the full paper (PDF)
942			_cERES
999			_c700 _d700