H-matrix (iterative method) explained

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.^[1]

See also

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

References

1. Zhang . Cheng-yi . Ye . Dan . Zhong . Cong-Lei . SHUANGHUA . SHUANGHUA . 2015 . Convergence on Gauss–Seidel iterative methods for linear systems with general H-matrices . The Electronic Journal of Linear Algebra . 30 . 843–870 . 10.13001/1081-3810.1972 . 21 June 2018 . 1410.3196 .