Conditioning analysis of positive definite matrices by approximate factorizations

摘要

The conditioning analysis of positive definite matrices by approximate LU factorizations is usually reduced to that of Stieltjes matrices (or even to more specific classes of matrices) by means of perturbation arguments like spectral equivalence. We show in the present work that a wider class, which we call “almost Stieltjes” matrices, can be used as reference class and that it has decisive advantages for the conditioning analysis of finite element approximations of large multidimensional steady-state diffusion problems.