- Lecture on Numerical Linear Algebra
- 12th floor, Lecture room 1 (Room 1212), National Institute of Informatics
- July 27th (Friday), 2-4pm
- H-matrices and their Schur complements
José Mas Marí (Professor, Departament de Matemàtica Aplicada, Universitat Politècnica de València, Spain)
What happens if the comparison matrix of a given matrix is a singular M-matrix? This question will be answered and characterizations of H-matrices with singular or nonsingular comparison matrix will be analyzed. In particular, the case of irreducible matrices will be analyzed and some insights into the reducible case will be given. The spectral radius of the Jacobi matrix of the comparison matrix and the generalized diagonal dominance property are used in the characterizations. Finally, from these characterizations, a partition of the general H-matrix set in three classes is obtained.
In the second part we will focus on the Schur complement of H-matrices. It is well-known that the Schur complement of some H-matrices is an H-matrix. We will study the Schur complement of any general H-matrixt. In particular it is proved that the Schur complement, if it exists, is an H-matrix and it is studied to which class of H-matrix the Schur complement belongs to. In addition, results are given for singular irreducible H-matrices and for the Schur complement of nonsingular irreducible H-matrices.
Contact: Ken Hayami(NII, firstname.lastname@example.org)