Stable computation of the Fourier transform using regularization
An ill-posed Fredholm integral equation of the first kind is considered. The \(n\)-order Tikhonov regularization method is employed to increase the stability of computing the Fourier transform. The regularization parameter \(\alpha\) is selected by the residual technique. The regularization of direct and inverse, continuous and discrete, and one- and two-dimensional Fourier transforms is discussed.
ill-posed Fredholm integral equation of the first kind
scientific article; zbMATH DE number 1467887