ISSN:
0945-3245
Keywords:
41A15
;
42A16
;
65D07
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Let be thek-dimensional subspace spanned by the translates ϕ(·−2πj/k),j=0, 1, ...,k−1, of a continuous, piecewise smooth, complexvalued, 2π-periodic function ϕ. For a given functionf∈L 2(−π, π), its least squares approximantS kf from can be expressed in terms of an orthonormal basis. Iff is continuous,S kf 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 include the space of trigonometric polynomials where ϕ is the de la Valleé Poussin kernel, algebraic polynomial splines where ϕ is the periodic B-spline, and trigonometric polynomial splines where ϕ is the trigonometric B-spline.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01385736
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