Geodesic
Gradient methods with improved convergence rate
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 374-382 
E. A. Alshina; A. A. Boltnev; O. A. Kacher. Gradient methods with improved convergence rate. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 374-382. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_3_a1/
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     title = {Gradient methods with improved convergence rate},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A very simple modification is proposed for the steepest descent and minimum residual methods that makes it possible to substantially improve the convergence rate of these methods. The proposed approach is universal and does not require any adjustment to the spectrum of a matrix. Its efficiency is confirmed by numerous computational experiments.

[1] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[2] Kalitkin H. H., Chislennye metody, Nauka, M., 1978 | MR

[3] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR | Zbl

[4] Golub Dzh., Van-Loun Ch., Matrichnye vychisleniya, Mir, M., 1999

[5] Daniel J. V., “The conjugate gradient method for linear and nonlinear operator equations”, SIAM J. Numer. Analys., 1:4 (1967), 10–26 | DOI | MR

[6] Swarztrauber P. N., “The method of cyclic reduction, Fourier analysis and the FARC algorithm for the discrete solution of Poisson's equation on a rectangle”, SIAM Rev., 110 (1976), 353–372

[7] Ermakov V. V., Kalitkin H. H., “Dvukhstupenchatyi gradientnyi spusk”, Zh. vychisl. matem. i matem. fiz., 20:4 (1980), 1040–1045 | MR | Zbl

[8] Kalitkin H. H., Litvintseva S. P., “Gradientnyi spusk so sluchainymi shagami”, Matem. modelirovanie, 9:7 (1997), 63–70 | MR | Zbl

[9] Chegis R. Yu., “O skorosti skhodimosti kombinirovannykh iteratsionnykh metodov variatsionnogo tipa”, Matem. modelirovanie, 9:4 (1997), 115–125 | MR

[10] Karatson J., “Constructive Sobolev gradient preconditioning for semilinear elliptic system”, Electron. J. Differenz. Equat., 2004, no. 75, 1–26 | MR

[11] Faddeev D. K., Faddeeva V. N., Vychislitelnye metody lineinoi algebry, Izd. 2-e, Fizmatgiz, M.–L., 1963 ; Изд. 3-е, Лань, СПб., 2002 | MR | Zbl