A necessary and sufficient condition for \(M\)-matrices and its relation to block \(LU\) factorization
The author reports necessary and sufficient conditions for \(M\)-matrices in terms of special diagonal dominance. He uses new results to show that if the comparison matrix for a block matrix is an \(M\)-matrix, there exists a stable block permutation matrix. Next, incomplete \(M\)-matrices are defined, necessary and sufficient conditions for such matrices are proved and their implication on block LU-factorization is presented.
scientific article; zbMATH DE number 871125
scientific article