Returning 'traditional' notations of functions in the context of fourier interpolation
问题 in numerical analysis we students are obligated to implement code in R that given a function f(x) finds its Fourier interpolation tN(x) and computes the interpolation error $||f(x)-t_{N}(x)||=\int_{0}^{2\pi}$ $|f(x)-t_{N}(x)|^2$ or a variety of different $N$ I first tried to compute the d-coefficients according to this formular: $d = \frac 1N M y$ with M denoting the DFT matrix and y denoting a series of equidistant function values with $y_j = f(x_j)$ and $x_j = e^{\frac{2*pi*i}N*j}$ for $j =