MEYER C. D. (2000). Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics. Home/Search Document Not in Database Summary Related Articles Check |
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....the algorithm. In either case, 5 it is natural to ask what kind of generalized inverse is being approximated by G when A is a singular matrix. It can be shown that the Moore Penrose pseudoinverse A y is the matrix of smallest Frobenius norm that minimizes jjI Gamma AXjj F ; see for instance [23], page 428. Hence, in the singular case the SPAI preconditioner can be seen as a sparse approximate Moore Penrose inverse of A. This is generally very different from the approximate (1; 2) inverses obtained by either ILU or AINV. In the next section we restrict our attention to the AINV ....
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