Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals.
New methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A1/2 or log(A) with singularities in (-∞, 0] and A is a matrix with eigenvalues on or near (0, ∞). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule wi...
| Үндсэн зохиолчид: | , , |
|---|---|
| Формат: | Journal article |
| Хэл сонгох: | English |
| Хэвлэсэн: |
2008
|
| _version_ | 1826278243084271616 |
|---|---|
| author | Hale, N Higham, N Trefethen, L |
| author_facet | Hale, N Higham, N Trefethen, L |
| author_sort | Hale, N |
| collection | OXFORD |
| description | New methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A1/2 or log(A) with singularities in (-∞, 0] and A is a matrix with eigenvalues on or near (0, ∞). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions. The convergence is geometric, so that the computation of f(A)fe is typically reduced to one or two dozen linear system solves, which can be carried out in parallel. © 2008 Society for Industrial and Applied Mathematics. |
| first_indexed | 2024-03-06T23:41:02Z |
| format | Journal article |
| id | oxford-uuid:6f50f9c3-34f8-4ac4-a23f-93f93496d22c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:41:02Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:6f50f9c3-34f8-4ac4-a23f-93f93496d22c2022-03-26T19:29:55ZComputing AAlpha, log(A), and Related Matrix Functions by Contour Integrals.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6f50f9c3-34f8-4ac4-a23f-93f93496d22cEnglishSymplectic Elements at Oxford2008Hale, NHigham, NTrefethen, LNew methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A1/2 or log(A) with singularities in (-∞, 0] and A is a matrix with eigenvalues on or near (0, ∞). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions. The convergence is geometric, so that the computation of f(A)fe is typically reduced to one or two dozen linear system solves, which can be carried out in parallel. © 2008 Society for Industrial and Applied Mathematics. |
| spellingShingle | Hale, N Higham, N Trefethen, L Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals. |
| title | Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals. |
| title_full | Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals. |
| title_fullStr | Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals. |
| title_full_unstemmed | Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals. |
| title_short | Computing AAlpha, log(A), and Related Matrix Functions by Contour Integrals. |
| title_sort | computing aalpha log a and related matrix functions by contour integrals |
| work_keys_str_mv | AT halen computingaalphalogaandrelatedmatrixfunctionsbycontourintegrals AT highamn computingaalphalogaandrelatedmatrixfunctionsbycontourintegrals AT trefethenl computingaalphalogaandrelatedmatrixfunctionsbycontourintegrals |