A minimal residual method for linear polynomials in unitary matrices
M. Danaa, 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, called MINRES-N2, that is based on the use of unconventional Krylov subspaces was previously proposed by the authors for solving a system of linear equations $Ax=b$ with a normal coefficient matrix whose spectrum belongs to an algebraic second-degree curve $\Gamma$. However, the computational scheme of this method does not cover matrices of the form
$A=\alpha U+\beta I$, where $U$ is an arbitrary unitary matrix; for such matrices, $\Gamma$ is a circle. Systems of this type are repeatedly solved when the eigenvectors of a unitary matrix are calculated by inverse iteration. In this paper, a modification of MINRES-N2 suitable for linear polynomials in unitary matrices is proposed. Numerical results are presented demonstrating the significant superiority of the modified method over GMRES as applied to systems of this class.
linear polynomials in unitary matrices, minimal residual method, modification of the MINRES-N2 algorithm.
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Computational Mathematics and Mathematical Physics, 2006, 46:6, 930–936
M. Dana, Kh. D. Ikramov, “A minimal residual method for linear polynomials in unitary matrices”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 975–982; Comput. Math. Math. Phys., 46:6 (2006), 930–936
Citation in format AMSBIB
\by M.~Dana, Kh.~D.~Ikramov
\paper A~minimal residual method for linear polynomials in unitary matrices
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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