Function lbcrypto::EvalChebyshevCoefficients

Function Documentation

std::vector<double> lbcrypto::EvalChebyshevCoefficients(std::function<double(double)> f, double a, double b, uint32_t d)

Method for calculating Chebyshev coefficients for an input function over the range [a,b]. These coefficents are used in EValChebyshevSeries to approximate the function func as func(x) ~ coeffs[0]/2 + sum_{i=1}^{degree} coeffs[i] * T_{i}(x), where T_{i}(x) are Chebyshev polynomials of the first kind. (Note that the 1st coeffiicent is divided by two.)

Parameters

  • func – is the function to be approximated

  • a – - lower bound of argument for which the coefficients were found

  • b – - upper bound of argument for which the coefficients were found

  • degree – Desired degree of approximation

Returns

the coefficients of the Chebyshev approximation.