Sparse discretization matrices for Volterra integral operators with applications to numerical differentiation
The authors study the numerical solution of Volterra integral equations of the first kind. It is supposed a finite dimensional feature space or, equivalently, that the integral kernel has finite rank. This allows the construction of orthonormal bases with small support that is preserved by the integral operator. In particular, the proposed method is based on the Tikhonov regularization and the projection method with respect to the constructed orthonormal basis that provides a sparse discretization of the Tikhonov operator. An example of a basis functions with the required properties are obtained by using wavelet bases. The paper concludes with the application of the proposed method to the solution of the integral equation arising from the numerical differentiation problem.
scientific article; zbMATH DE number 5915501
scientific article