Please use this identifier to cite or link to this item: https://doi.org/10.1007/BF01385736
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dc.titleL2-approximation by the translates of a function and related attenuation factors
dc.contributor.authorLee, S.L.
dc.contributor.authorTan, R.C.E.
dc.contributor.authorTang, W.S.
dc.date.accessioned2014-10-28T02:37:41Z
dc.date.available2014-10-28T02:37:41Z
dc.date.issued1991-12
dc.identifier.citationLee, S.L.,Tan, R.C.E.,Tang, W.S. (1991-12). L2-approximation by the translates of a function and related attenuation factors. Numerische Mathematik 60 (1) : 549-568. ScholarBank@NUS Repository. <a href="https://doi.org/10.1007/BF01385736" target="_blank">https://doi.org/10.1007/BF01385736</a>
dc.identifier.issn0029599X
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/103471
dc.description.abstractLet[Figure not available: see fulltext.] be the k-dimensional subspace spanned by the translates φ{symbol}(·-2πj/k), j=0, 1, ..., k-1, of a continuous, piecewise smooth, complexvalued, 2π-periodic function φ{symbol}. For a given function f∈L2(-π, π), its least squares approximant Skf from[Figure not available: see fulltext.] can be expressed in terms of an orthonormal basis. If f is continuous, Skf can be computed via its discrete analogue by fast Fourier transform. The discrete least squares approximant is used to approximate Fourier coefficients, and this complements the works of Gautschi on attenuation factors. Examples of[Figure not available: see fulltext.] include the space of trigonometric polynomials where φ{symbol} is the de la Valleé Poussin kernel, algebraic polynomial splines where φ{symbol} is the periodic B-spline, and trigonometric polynomial splines where φ{symbol} is the trigonometric B-spline. © 1992 Springer-Verlag.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1007/BF01385736
dc.sourceScopus
dc.subjectMathematics Subject Classification (1991): 41A15, 42A16, 65D07
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1007/BF01385736
dc.description.sourcetitleNumerische Mathematik
dc.description.volume60
dc.description.issue1
dc.description.page549-568
dc.identifier.isiutNOT_IN_WOS
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