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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.

See also

• Hurwitz-stable 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. arXiv:1410.3196. doi:10.13001/1081-3810.1972. Retrieved 21 June 2018.

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