Fast, numerically stable computation of oscillatory integrals with stationary points
We present a numerically stable way to compute oscillatory integrals of the form $\int{-1}^{1} f(x)e^{i\omega g(x)}dx$. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increa...
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| Fformat: | Report |
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Unspecified
2009
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| _version_ | 1826284808061321216 |
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| author | Olver, S |
| author_facet | Olver, S |
| author_sort | Olver, S |
| collection | OXFORD |
| description | We present a numerically stable way to compute oscillatory integrals of the form $\int{-1}^{1} f(x)e^{i\omega g(x)}dx$. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the first stable algorithm for oscillatory integrals with stationary points which does not lose accuracy as the frequency increases and does not require deformation into the complex plane. |
| first_indexed | 2024-03-07T01:19:24Z |
| format | Report |
| id | oxford-uuid:8fd27e51-cc38-4c87-944c-01d4b79aa59f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:19:24Z |
| publishDate | 2009 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:8fd27e51-cc38-4c87-944c-01d4b79aa59f2022-03-26T23:07:05ZFast, numerically stable computation of oscillatory integrals with stationary pointsReporthttp://purl.org/coar/resource_type/c_93fcuuid:8fd27e51-cc38-4c87-944c-01d4b79aa59fMathematical Institute - ePrintsUnspecified2009Olver, SWe present a numerically stable way to compute oscillatory integrals of the form $\int{-1}^{1} f(x)e^{i\omega g(x)}dx$. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the first stable algorithm for oscillatory integrals with stationary points which does not lose accuracy as the frequency increases and does not require deformation into the complex plane. |
| spellingShingle | Olver, S Fast, numerically stable computation of oscillatory integrals with stationary points |
| title | Fast, numerically stable computation of oscillatory integrals with stationary points |
| title_full | Fast, numerically stable computation of oscillatory integrals with stationary points |
| title_fullStr | Fast, numerically stable computation of oscillatory integrals with stationary points |
| title_full_unstemmed | Fast, numerically stable computation of oscillatory integrals with stationary points |
| title_short | Fast, numerically stable computation of oscillatory integrals with stationary points |
| title_sort | fast numerically stable computation of oscillatory integrals with stationary points |
| work_keys_str_mv | AT olvers fastnumericallystablecomputationofoscillatoryintegralswithstationarypoints |