The direct-projection methods
Zhongxuan Luo, B.P.B. Silva, Jinyun Yuan · International Journal of Computer Mathematics · 2001
In this paper, the direct-projection method given by Benzi and Meyer (1995) is derived by slightly different way - Basic Solutions of corresponding homogeneous system. The idea of the method differs from the idea of the Gaussian Elimination (or LU decomposition). The method works for every nonsingular coefficient matrix in the absence of rounding error. The Gaussian Elimination is explained by the method. The corresponding numerical algorithms of the method are also given. The method is applied to find the preconditioner for least squares problems and solvers of singular systems. The numerical experiments illustrate that the method has better numerical stability than the Gaussian Elimination.