Non-recursive equivalent of the conjugate gradient method without the need to restart

Autor:	Dvornik, Josip, Lazarevic, Damir, Lazarevic, Antonia Jaguljnjak, Demsic, Marija
Rok vydání:	2019
Předmět:	Computer Science - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	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 in n-dimensional space. Finally, relaxation factor and preconditioning-like techniques can be adopted easily. Comment: 9 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1903.11379 Zobrazit plný text záznamu View this record from Arxiv