On greedy randomized kaczmarz method for solving large sparse linear systems

Zhong Zhi Bai, Wen Ting Wu

Research output: Contribution to journalArticlepeer-review

150 Citations (Scopus)

Abstract

For solving large-scale systems of linear equations by iteration methods, we introduce an effective probability criterion for selecting the working rows from the coefficient matrix and construct a greedy randomized Kaczmarz method. It is proved that this method converges to the unique least-norm solution of the linear system when it is consistent. Theoretical analysis demonstrates that the convergence rate of the greedy randomized Kaczmarz method is much faster than the randomized Kaczmarz method, and numerical results also show that the greedy randomized Kaczmarz method is more efficient than the randomized Kaczmarz method.

Original languageEnglish
Pages (from-to)A592-A606
JournalSIAM Journal on Scientific Computing
Volume40
Issue number1
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • Convergence property
  • Kaczmarz method
  • Randomized iteration
  • System of linear equations

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