• Source: 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 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.




See also


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




References

Kata Kunci Pencarian:

• H-matrix (iterative method)
• Relaxation (iterative method)
• Quasi-Newton method
• Newton's method in optimization
• Newton's method
• Comparison matrix
• Generalized minimal residual method
• Sparse matrix
• Invertible matrix
• Conjugate gradient method