Comparison results on preconditioned GAOR methods for weighted linear least squares problems. (English) Zbl 1251.65054

Summary: We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerical example to confirm our theoretical results.


65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
Full Text: DOI


[1] J.-Y. Yuan, “Numerical methods for generalized least squares problems,” Journal of Computational and Applied Mathematics, vol. 66, no. 1-2, pp. 571-584, 1996. · Zbl 0858.65043
[2] J.-Y. Yuan and X.-Q. Jin, “Convergence of the generalized AOR method,” Applied Mathematics and Computation, vol. 99, no. 1, pp. 35-46, 1999. · Zbl 0961.65029
[3] M. T. Darvishi, P. Hessari, and J. Y. Yuan, “On convergence of the generalized accelerated overrelaxation method,” Applied Mathematics and Computation, vol. 181, no. 1, pp. 468-477, 2006. · Zbl 1148.65028
[4] M. T. Darvishi and P. Hessari, “On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices,” Applied Mathematics and Computation, vol. 176, no. 1, pp. 128-133, 2006. · Zbl 1101.65033
[5] M. T. Darvishi, P. Hessari, and B.-C. Shin, “Preconditioned modified AOR method for systems of linear equations,” International Journal for Numerical Methods in Biomedical Engineering, vol. 27, no. 5, pp. 758-769, 2011. · Zbl 1226.65023
[6] R. S. Varga, Matrix Iterative Analysis, vol. 27 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2000. · Zbl 0998.65505
[7] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, vol. 9 of Classics in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. · Zbl 0815.15016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.