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Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart

Author(s):



Medium: journal article
Language(s): English
Published in: Advances in Civil Engineering, , v. 2019
Page(s): 1-5
DOI: 10.1155/2019/7527590
Abstract:

A simple alternative to the conjugate gradient (CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on conjugacy; i.e., it is not necessary to maintain overall orthogonalities between various vectors from distant steps. This method is more stable than CG, and restarting techniques are not required. As in CG, only one matrix-vector multiplication is required per step with appropriate transformations. The algorithm is easily explained by energy considerations without appealing to theA-orthogonality inn-dimensional space. Finally, relaxation factor and preconditioning-like techniques can be adopted easily.

Copyright: © 2019 Josip Dvornik et al.
License:

This creative work has been published under the Creative Commons Attribution 4.0 International (CC-BY 4.0) license which allows copying, and redistribution as well as adaptation of the original work provided appropriate credit is given to the original author and the conditions of the license are met.

  • About this
    data sheet
  • Reference-ID
    10311733
  • Published on:
    17/04/2019
  • Last updated on:
    02/06/2021
 
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