ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS

Zhong Zhi Bai, Wen Ting Wu

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

For solving large-scale inconsistent systems of linear equations by iteration methods, with the application of the greedy randomized Kaczmarz method to a consistent augmented linear system, we find an appropriate balance between the updates of the two iteration vectors in the randomized extended Kaczmarz method, and, based on this balance, we propose a greedy randomized augmented Kaczmarz method. We prove the convergence of the greedy randomized augmented Kaczmarz method and derive an upper bound for its expected convergence rate. Numerical results show that the greedy randomized augmented Kaczmarz method can be much more effective than the randomized extended Kaczmarz method as well as the partially randomized extended Kaczmarz method.

Original languageEnglish
Pages (from-to)A3892-A3911
JournalSIAM Journal on Scientific Computing
Volume43
Issue number6
DOIs
Publication statusPublished - 2021

Keywords

  • Kaczmarz method
  • augmented linear system
  • convergence property
  • inconsistency
  • randomized iteration
  • system of linear equations

Fingerprint

Dive into the research topics of 'ON GREEDY RANDOMIZED AUGMENTED KACZMARZ METHOD FOR SOLVING LARGE SPARSE INCONSISTENT LINEAR SYSTEMS'. Together they form a unique fingerprint.

Cite this