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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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On the solution of a class of Volterra integral equations of the first kind

F. Fagnani / L. Pandolfi

Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy. E-mails: ,

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 11, Issue 5, Pages 485–503, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939403770888237,

Publication History

Published Online:

In this paper we propose an iterative algorithm for the solution of Volterra equations of the first kind whose kernel is a square matrix. The algorithm, essentially the Lavrientev method coupled with discretization, is "direct" in the sense that preliminary numerical computation of the derivative of the observed variable is not required. We assume boundedness of the input u and mild regularity conditions of the kernel. We prove convergence of the algorithm in L p(0, T), 1 ≤ p < +∞ and uniform convergence on the intervals where the input is continuous.

Under additional information on u we give both integral and pointwise convergence estimates.

The observed variable is read with errors, at discrete time instants.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Luciano Pandolfi
Annual Reviews in Control, 2010, Volume 34, Number 2, Page 245
[2]
L. Pandolfi
International Journal of Control, 2007, Volume 80, Number 3, Page 403
[3]
A. Favini and L. Pandolfi
Numerical Functional Analysis and Optimization, 2008, Volume 29, Number 11-12, Page 1252
[4]
A. Favini and L. Pandolfi
Journal of Inverse and Ill-posed Problems, 2008, Volume 16, Number 3

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