Geodesic
The improved form of the conjugated gradients method
Matematičeskoe modelirovanie, Tome 23 (2011) no. 7, pp. 33-51

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The conjugated gradient method for systems of linear algebraic equations is investigated. The form of this method is constracted, which occured especially simple and stable under round-off errors. The criterium of iteration truncation is proposed based on prevailing of round-off errors. The numerical calculations were performed, illustrating peculiarities of the method convergency for good and ill posed problems.
Keywords: systems of linear algebraic equations, the conjugated gradients method, round-off errors, ill posed problems. 
@article{MM_2011_23_7_a2,
     author = {N. N. Kalitkin and L. V. Kuzmina},
     title = {The improved form of the conjugated gradients method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--51},
     publisher = {mathdoc},
     volume = {23},
     number = {7},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_7_a2/}
}
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N. N. Kalitkin; L. V. Kuzmina. The improved form of the conjugated gradients method. Matematičeskoe modelirovanie, Tome 23 (2011) no. 7, pp. 33-51. http://geodesic.mathdoc.fr/item/MM_2011_23_7_a2/