Discrete Transformation of Mesh Functions Values to Fourier Polynomials Coefficients

Here is elaborated the instrument for solving the practical task of serial reconstruction of coefficients of functions expansion by Zernike polynomials when knowing approximately measured their mesh values. A series of overdetermined and incompatible systems of linear algebraic equations with different right parts and matrices within one accuracy class is solved by Tikhonov regularization method. The conditions of the existence of unique pseudoinverse matrix for exact system are considered. The convergence of regularized pseudoinverse matrices to the exact one is proved when perturbation tends to zero.

разложение в ряд Фурье, система линейных алгебраических уравнений, регуляризация