SPARSE DISCRETIZATION MATRICES FORVOLTERRA INTEGRAL OPERATORS WITHAPPLICATIONS TO NUMERICAL DIFFERENTIATION

摘要

We consider Volterra integral equations hav-ing a finite dimensional feature space. This provides us flex-ibility to construct an orthonormal basis with small support that can be preserved by the Volterra integral operator. Un-der the projection method, such a basis yields a sparse dis-cretization matrix for the Volterra integral operator. When the feature space is refinable, we introduce a construction of such an orthonormal basis from existing references. Finally, we present applications to numerical differentiation for which we obtain a quasi-linear lossless compression of the discretiza-tion matrix.