This article is cited in 4 scientific papers (total in 4 papers)
A minimal residual method for a special class of linear systems with normal coefficients matrices
M. Danaa, A. G. Zykovb, Kh. D. Ikramovb
a Faculty of Mathematics, University of Kurdistan, Sanandage, 66177, Islamic Republic of Iran
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
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.
minimal residual method, system of linear algebraic equations, GMRES, MINRES.
PDF file (1438 kB)
Computational Mathematics and Mathematical Physics, 2005, 45:11, 1854–1863
M. Dana, A. G. Zykov, Kh. D. Ikramov, “A minimal residual method for a special class of linear systems with normal coefficients matrices”, Zh. Vychisl. Mat. Mat. Fiz., 45:11 (2005), 1928–1937; Comput. Math. Math. Phys., 45:11 (2005), 1854–1863
Citation in format AMSBIB
\by M.~Dana, A.~G.~Zykov, Kh.~D.~Ikramov
\paper A minimal residual method for a special class of linear systems with normal coefficients matrices
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
M. Dana, Kh. D. Ikramov, “Solving systems of linear equations whose matrices are low-rank perturbations of Hermitian matrices, revisited”, J. Math. Sci. (N. Y.), 141:6 (2007), 1608–1613
M. Dana, Kh. D. Ikramov, “A minimal residual method for linear polynomials in unitary matrices”, Comput. Math. Math. Phys., 46:6 (2006), 930–936
Kh. D. Ikramov, “Improved bounds for the recursion width in congruent type methods for solving systems of linear equations”, J. Math. Sci. (N. Y.), 165:5 (2010), 515–520
M. Ghasemi Kamalvand, Kh. D. Ikramov, “A method of congruent type for linear systems with conjugate-normal coefficient matrices”, Comput. Math. Math. Phys., 49:2 (2009), 203–216
|Number of views:|