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Statements

Subject Item: dbr:M-matrix
dbo:wikiPageWikiLink: dbr:H-matrix_(iterative_method)

Subject Item: dbr:Comparison_matrix
dbo:wikiPageWikiLink: dbr:H-matrix_(iterative_method)

Subject Item: dbr:H-matrix
dbo:wikiPageWikiLink: dbr:H-matrix_(iterative_method)
dbo:wikiPageDisambiguates: dbr:H-matrix_(iterative_method)

Subject Item: dbr:H-matrix_(iterative_method)
rdfs:label: H-matrix (iterative method)
rdfs:comment: 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.
dct:subject: dbc:Matrices
dbo:wikiPageID: 57726619
dbo:wikiPageRevisionID: 961674098
dbo:wikiPageWikiLink: dbr:L-matrix dbr:Invertible_matrix dbr:Comparison_matrix dbr:Z-matrix_(mathematics) dbr:Matrix_(mathematics) dbr:M-matrix dbr:Gauss–Seidel_method dbc:Matrices dbr:Iterative_method dbr:Perron–Frobenius_theorem dbr:P-matrix dbr:Hurwitz_matrix
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dbo:abstract: 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.
prov:wasDerivedFrom: wikipedia-en:H-matrix_(iterative_method)?oldid=961674098&ns=0
dbo:wikiPageLength: 1674
foaf:isPrimaryTopicOf: wikipedia-en:H-matrix_(iterative_method)

Subject Item: wikipedia-en:H-matrix_(iterative_method)
foaf:primaryTopic: dbr:H-matrix_(iterative_method)