A structure-preserving divide-and-conquer method for pseudosymmetric matrices
We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e., pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral division such that the method can be applied recursively to ac...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Society for Industrial and Applied Mathematics
2023
|
| _version_ | 1826311188045103104 |
|---|---|
| author | Benner, P Nakatsukasa, Y Penke, C |
| author_facet | Benner, P Nakatsukasa, Y Penke, C |
| author_sort | Benner, P |
| collection | OXFORD |
| description | We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e., pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral division such that the method can be applied recursively to achieve full diagonalization. The method is well suited for structured matrices that come up in computational quantum physics and chemistry. In this application context, additional definiteness properties guarantee a convergence of the matrix sign function iteration within two steps when Zolotarev functions are used. The steps are easily parallelizable. Furthermore, it is shown that the matrix decouples into symmetric definite eigenvalue problems after just one step of spectral division. |
| first_indexed | 2024-03-07T08:04:39Z |
| format | Journal article |
| id | oxford-uuid:20589d28-7aa8-45bd-9648-2744356ebd28 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:04:39Z |
| publishDate | 2023 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:20589d28-7aa8-45bd-9648-2744356ebd282023-10-23T12:10:38ZA structure-preserving divide-and-conquer method for pseudosymmetric matricesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:20589d28-7aa8-45bd-9648-2744356ebd28EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2023Benner, PNakatsukasa, YPenke, CWe devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e., pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral division such that the method can be applied recursively to achieve full diagonalization. The method is well suited for structured matrices that come up in computational quantum physics and chemistry. In this application context, additional definiteness properties guarantee a convergence of the matrix sign function iteration within two steps when Zolotarev functions are used. The steps are easily parallelizable. Furthermore, it is shown that the matrix decouples into symmetric definite eigenvalue problems after just one step of spectral division. |
| spellingShingle | Benner, P Nakatsukasa, Y Penke, C A structure-preserving divide-and-conquer method for pseudosymmetric matrices |
| title | A structure-preserving divide-and-conquer method for pseudosymmetric matrices |
| title_full | A structure-preserving divide-and-conquer method for pseudosymmetric matrices |
| title_fullStr | A structure-preserving divide-and-conquer method for pseudosymmetric matrices |
| title_full_unstemmed | A structure-preserving divide-and-conquer method for pseudosymmetric matrices |
| title_short | A structure-preserving divide-and-conquer method for pseudosymmetric matrices |
| title_sort | structure preserving divide and conquer method for pseudosymmetric matrices |
| work_keys_str_mv | AT bennerp astructurepreservingdivideandconquermethodforpseudosymmetricmatrices AT nakatsukasay astructurepreservingdivideandconquermethodforpseudosymmetricmatrices AT penkec astructurepreservingdivideandconquermethodforpseudosymmetricmatrices AT bennerp structurepreservingdivideandconquermethodforpseudosymmetricmatrices AT nakatsukasay structurepreservingdivideandconquermethodforpseudosymmetricmatrices AT penkec structurepreservingdivideandconquermethodforpseudosymmetricmatrices |