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- Hierarchical_matrix abstract "In numerical mathematics, hierarchical matrices (H-matrices)are used as data-sparse approximations of non-sparse matrices.While a sparse matrix of dimension can be represented efficiently in units of storageby storing only its non-zero entries, a non-sparse matrix would require units of storage, and using this typeof matrices for large problems would therefore be prohibitively expensive in terms of storage and computing time.Hierarchical matrices provide an approximation requiring only units of storage, where is aparameter controlling the accuracy of the approximation.In typical applications, e.g., when discretizing integral equationsor solving elliptic partial differential equations,a rank proportional to with a small constant is sufficient to ensure anaccuracy of .Compared to many other data-sparse representations of non-sparse matrices, hierarchical matrices offer a major advantage:the results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximatedin operations, where".
- Hierarchical_matrix wikiPageExternalLink AHMED.html.
- Hierarchical_matrix wikiPageExternalLink www.hlib.org.
- Hierarchical_matrix wikiPageExternalLink www.hlibpro.com.
- Hierarchical_matrix wikiPageID "33198000".
- Hierarchical_matrix wikiPageRevisionID "583820848".
- Hierarchical_matrix hasPhotoCollection Hierarchical_matrix.
- Hierarchical_matrix subject Category:Matrices.
- Hierarchical_matrix type Abstraction100002137.
- Hierarchical_matrix type Arrangement107938773.
- Hierarchical_matrix type Array107939382.
- Hierarchical_matrix type Group100031264.
- Hierarchical_matrix type Matrices.
- Hierarchical_matrix type Matrix108267640.
- Hierarchical_matrix comment "In numerical mathematics, hierarchical matrices (H-matrices)are used as data-sparse approximations of non-sparse matrices.While a sparse matrix of dimension can be represented efficiently in units of storageby storing only its non-zero entries, a non-sparse matrix would require units of storage, and using this typeof matrices for large problems would therefore be prohibitively expensive in terms of storage and computing time.Hierarchical matrices provide an approximation requiring only units of storage, where is aparameter controlling the accuracy of the approximation.In typical applications, e.g., when discretizing integral equationsor solving elliptic partial differential equations,a rank proportional to with a small constant is sufficient to ensure anaccuracy of .Compared to many other data-sparse representations of non-sparse matrices, hierarchical matrices offer a major advantage:the results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximatedin operations, where".
- Hierarchical_matrix label "Hierarchical matrix".
- Hierarchical_matrix sameAs m.0h6801n.
- Hierarchical_matrix sameAs Q17029389.
- Hierarchical_matrix sameAs Q17029389.
- Hierarchical_matrix sameAs Hierarchical_matrix.
- Hierarchical_matrix wasDerivedFrom Hierarchical_matrix?oldid=583820848.
- Hierarchical_matrix isPrimaryTopicOf Hierarchical_matrix.