H-matrix (iterative method)

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 $n \times n$ 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 $i \neq j, 1 \leq i,j \leq n$ and $α ij = | A ij |$ for all $i = j, 1 \leq i,j \leq n$ . If M(A) is a M-matrix, A is a H-matrix.

Invertible H-matrix guarentees convergence of Gauss-Seidel iterative methods.^[1]

References

^ 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. doi:10.13001/1081-3810.1972. Retrieved 21 June 2018.

[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. doi:10.13001/1081-3810.1972. Retrieved 21 June 2018.

[1]

See also

References