We consider the Volterra integral equation of the first kind for the derivative of a given function with one-side boundary conditions. We give a method to obtain the singular value expansion for the corresponding integral kernel. This singular value expansion can be used to give algorithms for the solution of the numerical differentiation problem. A numerical experiment shows the results obtained by a simple version of such algorithms.

The singular value expansion of the Volterra integral equation associated to a numerical differentiation problem

Egidi, Nadaniela;Maponi, Pierluigi
2018-01-01

Abstract

We consider the Volterra integral equation of the first kind for the derivative of a given function with one-side boundary conditions. We give a method to obtain the singular value expansion for the corresponding integral kernel. This singular value expansion can be used to give algorithms for the solution of the numerical differentiation problem. A numerical experiment shows the results obtained by a simple version of such algorithms.
2018
262
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/407100
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