| 词条 | H-matrix (iterative method) |
| 释义 |
In mathematics, an H-matrix is a matrix whose comparison matrix is an M-matrix. It is useful in iterative methods. Definition: Let {{math|1=A = (aij)}} be a {{math|n × n}} complex matrix. Then comparison matrix M(A) of complex matrix A is defined as {{math|1=M(A) = αij}} where {{math|1=αij = −{{!}}Aij{{!}}}} for all {{math|1=i ≠ j, 1 ≤ i,j ≤ n}} and {{math|1=αij = {{!}}Aij{{!}}}} for all {{math|1=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.[1]See also
References1. ^{{cite journal |last1= Zhang |first1= Cheng-yi |last2= Ye |first2= Dan |last3= Zhong |first3= Cong-Lei |last4= SHUANGHUA |first4= SHUANGHUA |year=2015 |title= Convergence on Gauss–Seidel iterative methods for linear systems with general H-matrices |journal=The Electronic Journal of Linear Algebra |volume=30 |pages=843–870 |doi=10.13001/1081-3810.1972 |url=http://repository.uwyo.edu/ela/vol30/iss1/54/ |accessdate=21 June 2018 }} {{linear-algebra-stub}} 1 : Matrices |
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