caa a22 4500 378854283 CHVBK 20180305123331.0 cr unu---uuuuu 161128e20031201xx s 000 0 eng 10.1515/156939403770888237 doi (NATIONALLICENCE)gruyter-10.1515/156939403770888237 On the solution of a class of Volterra integral equations of the first kind [Elektronische Daten] [F. Fagnani, L. Pandolfi] 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. Copyright 2003, Walter de Gruyter Fagnani F. Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy. E-mails: fagnani@calvino.polito.it, lucipan@polito.it aut Pandolfi L. Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy. E-mails: fagnani@calvino.polito.it, lucipan@polito.it aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/5(2003-12-01), 485-503 0928-0219 11:5<485 2003 11 jiip https://doi.org/10.1515/156939403770888237 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403770888237 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fagnani F. Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy. E-mails: fagnani@calvino.polito.it, lucipan@polito.it aut NATIONALLICENCE 700 1- Pandolfi L. Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy. E-mails: fagnani@calvino.polito.it, lucipan@polito.it aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/5(2003-12-01), 485-503 0928-0219 11:5<485 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter