Volume singular integral equations are considered that describe the problems of the scattering of electromagnetic waves by bounded, inhomogeneous, and anisotropic dielectric structures. To discretize the equations, the collocation method on an uneven grid is used. To quickly multiply the matrix of the resulting SLAE by a vector, a uniform grid is introduced. Using algorithms for interpolating functions and the fast discrete Fourier transform, an algorithm for multiplying the SLAE matrix by a vector with the number of operations for its implementation is almost proportional to the dimension of the matrix. In addition, the amount of memory for implementing the algorithm is also proportional to the dimension.