3.2 Representation forms for a
trigonometric polynomialLet us consider the 2[pi]-periodic
trigonometric polynomial operator (or summability operator)
Teslic, "Comparative analysis of error distribution for symmetric hysteresis loop curves approximation by means of cosine and
trigonometric polynomial", presented at the 2nd Int.
For instance, Han presented the quadratic [6] and cubic [7]
trigonometric polynomial curves with a shape parameter.
Since the smooth periodic function Fp can be approximated well by the partial sum of its Fourier series [5,7,10], from this inequality, we see that we have constructed a
trigonometric polynomial [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which can approximate to f on [OMEGA] very well.
Han, "Piecewise quadratic
trigonometric polynomial curves," Mathematics of Computation, vol.
The subdivision scheme is called vector subdivision scheme if the corresponding subdivision symbol is a matrix of
trigonometric polynomial. Note that the vector subdivision scheme plays an important role in multiwavelet and multichannel wavelets analysis; see [3-5] and references therein.
N]]) return(p) The Get_JN function finds the
trigonometric polynomial of order N for the function f.
The symbol of the sequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is the
trigonometric polynomialThe Ij and Wr were ordered by sampling date (t) and gender, and a Fourier
trigonometric polynomial (Rey Pastor et al., 1987) using the least--squares technique was fitted:
To find expressions for both r(t) and s(t) (and assuming they have a
trigonometric polynomial representation (cf.
which is just the
trigonometric polynomial in Weierstrass's first approximation theorem.
