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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 = be a n × n complex matrix. Then comparison matrix M of complex matrix A is defined as M = αij where αij = −|Aij| for all i ≠ j, 1 ≤ i,j ≤ n and αij = |Aij| for all i = j, 1 ≤ i,j ≤ n. If M is a M-matrix, A is a H-matrix.
Invertible H-matrix guarantees convergence of Gauss–Seidel iterative methods.
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