The exponentially convergent trapezoidal rule
It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all acros...
| Main Authors: | , |
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| Format: | Report |
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SIAM
2013
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| _version_ | 1826292994889744384 |
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| author | Trefethen, L Weideman, J |
| author_facet | Trefethen, L Weideman, J |
| author_sort | Trefethen, L |
| collection | OXFORD |
| description | It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators. |
| first_indexed | 2024-03-07T03:23:16Z |
| format | Report |
| id | oxford-uuid:b82a6442-da54-4595-a3e9-688b4048facc |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:23:16Z |
| publishDate | 2013 |
| publisher | SIAM |
| record_format | dspace |
| spelling | oxford-uuid:b82a6442-da54-4595-a3e9-688b4048facc2022-03-27T04:53:58ZThe exponentially convergent trapezoidal ruleReporthttp://purl.org/coar/resource_type/c_93fcuuid:b82a6442-da54-4595-a3e9-688b4048faccMathematical Institute - ePrintsSIAM2013Trefethen, LWeideman, JIt is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators. |
| spellingShingle | Trefethen, L Weideman, J The exponentially convergent trapezoidal rule |
| title | The exponentially convergent trapezoidal rule |
| title_full | The exponentially convergent trapezoidal rule |
| title_fullStr | The exponentially convergent trapezoidal rule |
| title_full_unstemmed | The exponentially convergent trapezoidal rule |
| title_short | The exponentially convergent trapezoidal rule |
| title_sort | exponentially convergent trapezoidal rule |
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