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The kernel of a rule of approximate integration
| Content Provider | Scilit |
|---|---|
| Author | Loxton, J. H. Sanders, J. W. |
| Copyright Year | 1979 |
| Description | It is well known that the trapezoidal rule of quadrature is exact for linear functions on [0, 1], and easy to see that it is exact for functions of the form f = l+g where l is linear and g is odd about ½. Not so well known is an example of a continuous function for which the trapezoidal rule is exact but which does not have this form. In this paper we show that if the trapezoidal rule is exact for f then f has the form above provided it has either absolutely convergent Fourier series or continuous second derivative. We consider one-sided versions in which the approximate integrals are non-negative, and also characterize those sequences arising as the approximate integrals of a function with absolutely convergent Fourier series. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7DFC2523A6E0A15DBE2F411262605F42/S0334270000002356a.pdf/div-class-title-the-kernel-of-a-rule-of-approximate-integration-div.pdf |
| Ending Page | 267 |
| Page Count | 11 |
| Starting Page | 257 |
| ISSN | 03342700 |
| e-ISSN | 18394078 |
| DOI | 10.1017/s0334270000002356 |
| Journal | The Journal of the Australian Mathematical Society. Series B. Applied Mathematics |
| Issue Number | 3 |
| Volume Number | 21 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1980-01-01 |
| Access Restriction | Open |
| Subject Keyword | The Journal of the Australian Mathematical Society. Series B. Applied Mathematics Applied Mathematics Approximate Integrals Well Known Trapezoidal Rule |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
