H-matrix (iterative method) (original) (raw)
In mathematics, an H-matrix is a matrix whose comparison matrix is an M-matrix. It is useful in iterative methods. Definition: Let A = (aij) be a n × n complex matrix. Then comparison matrix M(A) of complex matrix A is defined as M(A) = 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(A) is a M-matrix, A is a H-matrix. Invertible H-matrix guarantees convergence of Gauss–Seidel iterative methods.