Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 93

A matrix A is said to be reducible if there exists a permutation matrix P such that:

The matrix A is called irreducible if no such permutation matrix exists.

The matrix A is said to be diagonally dominant if:

(5.21)

Some results that are used in PDE applications are:

1 If A is strictly diagonally dominant, then it is invertible.

2 If A is irreducible and diagonally dominant and if for at least one j, then A is invertible.