H-matrix (iterative method)

In mathematics, an H-matrix is a matrix whose comparison matrix is an M-matrix. It is useful in iterative methods.

Definition: Let $A = (a_{ij})$ be a $n × n$ complex matrix. Then comparison matrix M(A) of complex matrix A is defined as $M(A) = α_{ij}$ where $α_{ij} = −|A_{ij}|$ for all $i ≠ j, 1 ≤ i,j ≤ n$ and $α_{ij} = |A_{ij}|$ for all $i = j, 1 ≤ i,j ≤ n$. If M(A) is a M-matrix, A is a H-matrix.

Invertible H-matrix guarantees convergence of Gauss–Seidel iterative methods.