The envelope of the error for trigonometric and Chebyshev interpolation
dc.contributor.author | Boyd, John P. | en_US |
dc.date.accessioned | 2006-09-11T15:31:47Z | |
dc.date.available | 2006-09-11T15:31:47Z | |
dc.date.issued | 1990-12 | en_US |
dc.identifier.citation | Boyd, John P.; (1990). "The envelope of the error for trigonometric and Chebyshev interpolation." Journal of Scientific Computing 5(4): 311-363. <http://hdl.handle.net/2027.42/44984> | en_US |
dc.identifier.issn | 0885-7474 | en_US |
dc.identifier.issn | 1573-7691 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/44984 | |
dc.description.abstract | The error in Chebyshev or Fourier interpolation is the product of a rapidly varying factor with a slowly varying modulation. This modulation is the “envelope” of the error. Because this slow modulation controls the amplitude of the error, it is crucial to understand this “error envelope.” In this article, we show that the envelope varies strongly with x , but its variations can be predicted from the convergence-limiting singularities of the interpolated function f( x ). In turn, this knowledge can be translated into a simple spectral correction algorithm for wringing more accuracy out of the same pseudospectral calculation of the solution to a differential equation. | en_US |
dc.format.extent | 2104704 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers-Plenum Publishers; Plenum Publishing Corporation ; Springer Science+Business Media | en_US |
dc.subject.other | Fourier Method | en_US |
dc.subject.other | Pseudospectral Method | en_US |
dc.subject.other | Algorithms | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Computational Mathematics and Numerical Analysis | en_US |
dc.subject.other | Mathematical and Computational Physics | en_US |
dc.subject.other | Appl.Mathematics/Computational Methods of Engineering | en_US |
dc.subject.other | Interpolation Error | en_US |
dc.subject.other | Chebyshev Method | en_US |
dc.title | The envelope of the error for trigonometric and Chebyshev interpolation | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Science (General) | en_US |
dc.subject.hlbsecondlevel | Education | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Atmospheric, Oceanic & Space Science, Laboratory for Scientific Computation, University of Michigan, 2200 Bonisteel Boulevard, 48109, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/44984/1/10915_2005_Article_BF01063120.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF01063120 | en_US |
dc.identifier.source | Journal of Scientific Computing | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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