Inversion of First Kind Volterra Equations: Back to Direct Methods?

Numerical inversion of the first kind Volterra equation (the Abel inversion included) has been extensively studied. Direct methods were probably the first methods used to attempt the inversion. Together with the computer hardware evolution, new methods were devised in order to deal with the inherent...

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Autores principales: Bilbao, L.E., Grondona, D.E.
Formato: JOUR
Materias:
Abel equation
Direct method
Error propagation
First kind Volterra equations
Matrix method
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09320784_v48_n11_p1119_Bilbao
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_09320784_v48_n11_p1119_Bilbao
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spelling todo:paper_09320784_v48_n11_p1119_Bilbao2023-10-03T15:48:31Z Inversion of First Kind Volterra Equations: Back to Direct Methods? Bilbao, L.E. Grondona, D.E. Abel equation Direct method Error propagation First kind Volterra equations Matrix method Numerical inversion of the first kind Volterra equation (the Abel inversion included) has been extensively studied. Direct methods were probably the first methods used to attempt the inversion. Together with the computer hardware evolution, new methods were devised in order to deal with the inherent problem of this kind of equation, that is, error magnification. Using a large number of data points (several thousands) most methods are difficult to use, specially when the inversion and its error are required on line, that is, while performing the experiments. Further, error propagation (coming from the input data and from the parameters of the problem) is, usually, a difficult task and has not been extensively studied. On the other hand, direct methods together with an adequate filter give good resolution, are fast, and error propagation is easily performed. In this work we used the so called Matrix Method for inverting three different equations, showing how to build the resolvent nucleus and how errors propagate through the solution. © 1993, Walter de Gruyter. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09320784_v48_n11_p1119_Bilbao
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Abel equation
Direct method
Error propagation
First kind Volterra equations
Matrix method
spellingShingle Abel equation
Direct method
Error propagation
First kind Volterra equations
Matrix method
Bilbao, L.E.
Grondona, D.E.
Inversion of First Kind Volterra Equations: Back to Direct Methods?
topic_facet Abel equation
Direct method
Error propagation
First kind Volterra equations
Matrix method
description Numerical inversion of the first kind Volterra equation (the Abel inversion included) has been extensively studied. Direct methods were probably the first methods used to attempt the inversion. Together with the computer hardware evolution, new methods were devised in order to deal with the inherent problem of this kind of equation, that is, error magnification. Using a large number of data points (several thousands) most methods are difficult to use, specially when the inversion and its error are required on line, that is, while performing the experiments. Further, error propagation (coming from the input data and from the parameters of the problem) is, usually, a difficult task and has not been extensively studied. On the other hand, direct methods together with an adequate filter give good resolution, are fast, and error propagation is easily performed. In this work we used the so called Matrix Method for inverting three different equations, showing how to build the resolvent nucleus and how errors propagate through the solution. © 1993, Walter de Gruyter. All rights reserved.
format JOUR
author Bilbao, L.E.
Grondona, D.E.
author_facet Bilbao, L.E.
Grondona, D.E.
author_sort Bilbao, L.E.
title Inversion of First Kind Volterra Equations: Back to Direct Methods?
title_short Inversion of First Kind Volterra Equations: Back to Direct Methods?
title_full Inversion of First Kind Volterra Equations: Back to Direct Methods?
title_fullStr Inversion of First Kind Volterra Equations: Back to Direct Methods?
title_full_unstemmed Inversion of First Kind Volterra Equations: Back to Direct Methods?
title_sort inversion of first kind volterra equations: back to direct methods?
url http://hdl.handle.net/20.500.12110/paper_09320784_v48_n11_p1119_Bilbao
work_keys_str_mv AT bilbaole inversionoffirstkindvolterraequationsbacktodirectmethods
AT grondonade inversionoffirstkindvolterraequationsbacktodirectmethods
_version_ 1807319247156674560

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