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Fitting of a noisy curve by an asymmetrical peak model, with an iterative process (Gauss–Newton algorithm with variable damping factor α).Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints.
In applied mathematics, the non-uniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both).
An advantage of traditional polynomial regression is that the inferential framework of multiple regression can be used (this also holds when using other families of basis functions such as splines). A final alternative is to use kernelized models such as support vector regression with a polynomial kernel.
For interpolation using a small number of measurements, the series expansion with = has been found to be accurate within 1 mK over the calibrated range. Some authors recommend using =. [4] If there are many data points, standard polynomial regression can also generate accurate curve fits. Some manufacturers have begun providing regression ...
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which can be proved using the series definition of the polylogarithm and the orthogonality of the exponential terms (see e.g. discrete Fourier transform). Another important property, the inversion formula, involves the Hurwitz zeta function or the Bernoulli polynomials and is found under relationship to other functions below.
Naturally, one might expect from Weierstrass' theorem that using more points would lead to a more accurate reconstruction of f(x). However, this particular set of polynomial functions P n ( x ) is not guaranteed to have the property of uniform convergence; the theorem only states that a set of polynomial functions exists, without providing a ...
Many applications for Chebyshev nodes, such as the design of equally terminated passive Chebyshev filters, cannot use Chebyshev nodes directly, due to the lack of a root at 0. However, the Chebyshev nodes may be modified into a usable form by translating the roots down such that the lowest roots are moved to zero, thereby creating two roots at ...