Geodesic
A minimal residual method for a special class of linear systems with normal coefficients matrices
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1928-1937 Cet article a éte moissonné depuis la source Math-Net.Ru

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A minimal residual method is constructed for the class of linear systems with normal coefficient matrices whose spectra belong to algebraic curves of a low order $k$. From the well-known GMRES algorithm, the proposed method differs by the choice of the subspaces in which approximate solutions are sought; as a consequence, the latter method is described by a short-term recurrence. The case $k=2$ is discussed at length. Numerical results are presented that confirm the significant superiority of the proposed method over the GMRES as applied to the linear systems specified above. 
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M. Dana; A. G. Zykov; Kh. D. Ikramov. A minimal residual method for a special class of linear systems with normal coefficients matrices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1928-1937. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a2/

[1] Paige C. C., Saunders M. A., “Solution of sparse indefinite systems of linear equations”, SIAM J. Numer. Analys., 12 (1975), 617–629 | DOI | MR | Zbl

[2] Saad Y., Schultz M. H., “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems”, SIAM J. Sci. Statist. Comput., 7 (1986), 856–869 | DOI | MR | Zbl

[3] Elsner L., Ikramov Kh. D., “On a condensed form for normal matrices under finite sequences of elementary unitary similarities”, Linear Algebra Appl., 254 (1997), 79–98 | DOI | MR | Zbl

[4] Ikramov Kh. D., Elzner L., “O matritsakh, dopuskayuschikh unitarnoe privedenie k lentochnomu vidu”, Matem. zametki, 64:6 (1998), 871–880 | MR | Zbl

[5] Jagels C. F., Reichel L., “A fast minimal residual algorithm for shifted unitary matrices”, Numer. Linear Algebra Appl., 1 (1994), 555–570 | DOI | MR | Zbl

[6] Demmel Dzh., Vychislitelnaya lineinaya algebra. Teoriya i prilozheniya, Mir, M., 2001