On the relaxed greedy deterministic row and column iterative methods

03/29/2022
by   Nian-Ci Wu, et al.
0

For solving the large-scale linear system by iteration methods, we utilize the Petrov-Galerkin conditions and relaxed greedy index selection technique and provide two relaxed greedy deterministic row (RGDR) and column (RGDC) iterative methods, in which one special case of RGDR reduces to the fast deterministic block Kaczmarz method proposed in Chen and Huang (Numer. Algor., 89: 1007-1029, 2021). Our convergence analyses reveal that the resulting algorithms all have the linear convergence rates, which are bounded by the explicit expressions. Numerical examples show that the proposed algorithms are more effective than the relaxed greedy randomized row and column iterative methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/05/2020

A Novel Greedy Kaczmarz Method For Solving Consistent Linear Systems

With a quite different way to determine the working rows, we propose a n...
research
12/07/2019

Greed Works: An Improved Analysis of Sampling Kaczmarz-Motkzin

Stochastic iterative algorithms have gained recent interest in machine l...
research
04/10/2021

Convergence of Adaptive, Randomized, Iterative Linear Solvers

Deterministic and randomized, row-action and column-action linear solver...
research
04/06/2020

Greedy Block Gauss-Seidel Methods for Solving Large Linear Least Squares Problem

With a greedy strategy to construct control index set of coordinates fir...
research
12/13/2022

On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods

For solving a consistent system of linear equations, the classical row-a...
research
10/12/2022

Relaxed Kacanov scheme for the p-Laplacian with large p

We introduce a globally convergent relaxed Kacanov scheme for the comput...
research
05/27/2019

Parallel and Communication Avoiding Least Angle Regression

We are interested in parallelizing the Least Angle Regression (LARS) alg...

Please sign up or login with your details

Forgot password? Click here to reset