Editing Trigonometric interpolation (section)

==Formulation of the interpolation problem==
A trigonometric polynomial of degree ''K'' has the form
{{NumBlk|:|<math> p(x) = a_0 + \sum_{k=1}^K a_k \cos(kx) + \sum_{k=1}^K b_k \sin(kx). \,  </math>|{{EquationRef|1}}}}
This expression contains 2''K'' + 1 coefficients, ''a''<sub>0</sub>, ''a''<sub>1</sub>, … ''a''<sub>''K''</sub>, ''b''<sub>1</sub>, …, ''b''<sub>''K''</sub>, and we wish to compute those coefficients so that the function passes through ''N'' points:
:<math> p(x_n) = y_n, \quad n=0, \ldots, N-1. \, </math>
Since the trigonometric polynomial is periodic with period 2π, the ''N'' points can be distributed and ordered in one period as 
:<math> 0 \leq x_0 < x_1 < x_2 < \ldots  < x_{N-1} < 2  \pi. \, </math>
(Note that we do ''not'' in general require these points to be equally spaced.) The interpolation problem is now to find coefficients such that the trigonometric polynomial ''p'' satisfies the interpolation conditions.