Using trigonometric wavelets as trial functions and Galerkin method

the obtained stiffness matrix from discretization the hypersingular integral equation is symmetrical and circulant

which leads us to a fast numerical method based on fast Fourier transform. Furthermore

this method dont need to compute the entries of the stiffness matrix and overcome the drawback to solve generalized inverse matrix. The example states that it still has good accuracy when the accurate solution is almost singular.