Geodesic
New version of line-by-line recursive method for solving a~difference elliptical equations
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2010), pp. 20-27

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We consider a new version of the closure equation for the line-by-line recursive method. The equation is a double-point linear connection of the desired solution’s values in the neighboring nodes of the area grid. A special feature of the considered closure is asymptotically exact value of the equation factors in the case when the solution converges. Higher efficiency of the discussed version of the line-by-line recursive method for solving systems of linear algebraic equations with ill-conditioned matrices as compared with its previous versions is demonstrated by examples of model problem solutions.
Keywords: system of linear algebraic equations, iteration method, closure equations. 
@article{VTGU_2010_2_a2,
     author = {A. A. Fomin and L. N. Fomina},
     title = {New version of line-by-line recursive method for solving a~difference elliptical equations},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {20--27},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2010_2_a2/}
}
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A. A. Fomin; L. N. Fomina. New version of line-by-line recursive method for solving a~difference elliptical equations. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2010), pp. 20-27. http://geodesic.mathdoc.fr/item/VTGU_2010_2_a2/