Extension of Range of MINRES-CN Algorithm

DOI: 10.4236/am.2011.212205   PDF   HTML     3,678 Downloads   6,244 Views  


MINRES-CN is an iterative method for solving systems of linear equations with conjugate-normal coefficient matrices whose conspectra are located on algebraic curves of a low degree. This method was proposed in a previous publication of author and KH. D. Ikramov. In this paper, the range of applicability of MINRES-CN is extended in new direction. These are conjugate normal matrices that are low rank perturbations of Symmetric matrices. Examples are given that demonstrate a higher efficiency of MINRES-CN for this class of systems compared to the well-known algorithm GMRES.

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M. Kamalvand, "Extension of Range of MINRES-CN Algorithm," Applied Mathematics, Vol. 2 No. 12, 2011, pp. 1446-1447. doi: 10.4236/am.2011.212205.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. G. Kamalvand and Kh. D. Ikramov, “A Method of the Congruent Type for Linear Systems with Conjugate-Normal Coefficient Matrices,” Computational Mathematics and Mathematical Physics, Vol. 49, No. 2, 2009, pp. 203-216. doi:10.1134/S0965542509020018
[2] H. Fassbender and Kh. D. Ikramov, “Some Observations on the Youla Form and Conjugate-Normal Matrices,” Linear Algebra and its Applications, Vol. 422, No. 1, 2007, pp. 29-38. doi:10.1016/j.laa.2006.09.004
[3] R. A. Horn and C. R. Johnson, “Matrix Analysis,” Cambridge University Press, Cambridge, 1985

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