Chebyshev

Description

This function calculates a partial Chebyshev expansion

n=0NanTn(a+bx)

where an are the expansion coefficients and Tn(x) are Chebyshev polynomials of the first kind defined by the reccurence relation

T0(x)=1
T1(x)=x
Tn+1(x)=2xTn(x)Tn1(x)

Coefficients a and b are defined to map the fitting interval into [-1,1] interval.

Chebyshev function has tree attributes (non-fitting parameters). First is ‘n’ which has integer type and sets the expansion order and creates n+1 expansion coefficients (fitting parameters). The parameter names have the form ‘Ai’ where ‘A’ is letter ‘A’ and ‘i’ is the parameter’s index starting from 0.

The other two attributes are doubles ‘StartX’ and ‘EndX’ which define the expansion (fitting) interval.

Attributes (non-fitting parameters)

Name

Type

Default

Description

EndX

StartX

n

Properties (fitting parameters)

Name

Default

Description

A0

0.0

Categories: FitFunctions | Background

Source

C++ header: Chebyshev.h

C++ source: Chebyshev.cpp