Geodesic
On the Craig method convergency for linear algebraic systems
Matematičeskoe modelirovanie, Tome 24 (2012) no. 3, pp. 113-136.

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The iterative Craig method permits to solve linear algebraic systems with nonsymmetric (and even rectangular) matrix. The simple form of this method was constracted. The convergention this method was inverstigated on tests. The comparison with the conjugated gradients method was fulfeeld. It occurred that round of errors for the Craig method decelerate essentially iterations convergence, but not prevent from high accuracy achievement (for well conditioned matrixes). The effective criterium is found for iterations truncation.
Keywords: linear algebraic systems, the Craig method, iterations convergency, round of errors. 
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N. N. Kalitkin; L. V. Kuzmina. On the Craig method convergency for linear algebraic systems. Matematičeskoe modelirovanie, Tome 24 (2012) no. 3, pp. 113-136. http://geodesic.mathdoc.fr/item/MM_2012_24_3_a8/

[1] Faddeev D. K., Faddeeva V. N., Vychislitelnye metody lineinoi algebry, Fizmatgiz, M., 1960 | MR

[2] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka. Fizmatlit, M., 1978, 592 pp. | MR

[3] Craig E., “The N-step iteration procedures”, J. Math. and Phys., 34:1 (1955), 64–73 | MR | Zbl

[4] Abramov A. A., Ulyanova V. I., Yukhno L. F., “O primenenii metoda Kreiga k resheniyu lineinykh uravnenii s netochno zadannymi iskhodnymi dannymi”, ZhVMiMF, 42:12 (2002), 1763–1770 | MR | Zbl

[5] Kalitkin N. N., Yukhno L. F., Kuzmina L. V., “Kriterii obuslovlennosti sistem algebraicheskikh uravnenii”, DAN, 434:4 (2010), 464–467 | MR | Zbl

[6] Kalitkin N. N., Yukhno L. F., Kuzmina L. V., “Kolichestvennyi kriterii obuslovlennosti sistem lineinykh algebraicheskikh uravnenii”, Matemat. modelirovanie, 23:2 (2011), 3–26 | MR | Zbl

[7] Kalitkin N. N., Kuzmina L. V., “Uluchshennaya forma metoda sopryazhennykh gradientov”, Matematicheskoe modelirovanie, 23:7 (2011), 33–51 | MR | Zbl

[8] Yukhno L. F., “Modifikatsiya nekotorykh metodov tipa sopryazhennykh napravlenii dlya resheniya sistem lineinykh algebraicheskikh uravnenii”, ZhVMiMF, 47:11 (2007), 1811–1818 | MR

[9] Kalitkin N. N., Kuzmina L. V., “Ob approksimatsii neortogonalnymi sistemami”, Matematicheskoe modelirovanie, 16:3 (2004), 95–108 | MR | Zbl