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 be a complex matrix. Then comparison matrix M(A) of complex matrix A is defined as where for all and for all . If M(A) is a M-matrix, A is a H-matrix.

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

See also

• Hurwitz-stable matrix
• P-matrix
• Perron–Frobenius theorem
• Z-matrix
• L-matrix
• M-matrix
• Comparison matrix

References