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Krylov subspace methods with deflation and balancing preconditioners for least squares problems
Liang Zhao,Ting-Zhu Huang,Liu Zhu,Liang-Jian Deng
Keywords:Least squares problems; Krylov subspace methods; Deflation preconditioner; Balancing preconditioner
      For solving least squares problems, the CGLS method is a typical method in the point of view of iterative methods. When the least squares problems are ill-conditioned, the convergence behavior of the CGLS method will present a deteriorated result. We expect to select other iterative Krylov subspace methods to overcome the disadvantage of the CGLS method. Here the GMRES method is a suitable algorithm for the reason that it is derived from the minimal residual norm approach, which coincides with least squares problems. We utilize preconditioned Krylov subspace iterative methods with deflation and balancing preconditioners in order to solve ill-conditioned least squares problems. Numerical experiments show that the methods proposed in this paper are better than the CGLS method.