A numerical comparison of two minimal residual methods for linear polynomials in unitary matrices

M. Dana^a, Kh. D. Ikramov<sup>b

a</sup> 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

Abstract: Two minimal residual methods for solving linear systems of the form $(\alpha U+\beta I)x=b$, where $U$ is a unitary matrix, are compared numerically. The first method uses conventional Krylov subspaces, while the second involves generalized Krylov subspaces. Experiments favor the second method if $|\alpha|>|\beta|$. Moreover, the greater the ratio $|\alpha|/|\beta|$, the higher the superiority of the second method.

Key words: Krylov subspace methods, minimal residual methods, normal matrices, unitary matrices.

UDC: 519.61

Received: 26.06.2006

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:12, 2040–2050

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