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

 Auteur(s): Josip Dvornik Damir Lazarević Antonia Jaguljnjak Lazarevic Marija Demsic article de revue anglais Advances in Civil Engineering, 2019, v. 2019 1-5 10.1155/2019/7527590 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 the$A$-orthogonality inn-dimensional space. Finally, relaxation factor and preconditioning-like techniques can be adopted easily. © 2019 Josip Dvornik et al. Cette oeuvre a été publiée sous la license Creative Commons Attribution 4.0 (CC-BY 4.0). Il est autorisé de partager et adapter l'oeuvre tant que l'auteur est crédité et la license est indiquée (avec le lien ci-dessus). Vous devez aussi indiquer si des changements on été fait vis-à-vis de l'original.
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• Reference-ID
10311733
• Publié(e) le:
17.04.2019
• Modifié(e) le:
02.06.2021