Abstract:
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.
Registro:
Documento: |
Artículo
|
Título: | Inversion of First Kind Volterra Equations: Back to Direct Methods? |
Autor: | Bilbao, L.E.; Grondona, D.E. |
Filiación: | Instituto de Física del Plasma, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
|
Palabras clave: | Abel equation; Direct method; Error propagation; First kind Volterra equations; Matrix method |
Año: | 1993
|
Volumen: | 48
|
Número: | 11
|
Página de inicio: | 1119
|
Página de fin: | 1130
|
DOI: |
http://dx.doi.org/10.1515/zna-1993-1111 |
Título revista: | Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
|
Título revista abreviado: | Z. Naturforsch. Sect. A J. Phys. Sci.
|
ISSN: | 09320784
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09320784_v48_n11_p1119_Bilbao |
Referencias:
- Mather, J., (1971) Dense Plasma Focus, Plasma Physics, 9 b, p. 187. , (R. Lovberg and H. Griem, eds.), Academic Press, New York
- Landeburg, R., Bershader, D., (1954) Interferometry, in: Physical Measurements in Gas Dynamics and Combustion, 9, p. 47. , High Speed Aerodynamics and Jet Propulsion, Princeton University Press, Princeton, New Jersey
- Morgan, P., (1974) Optical refractivities studies of plasma focus, , Ph.D. Thesis, University of London
- Bruzzone, H., Moreno, C., Kelly, H., (1991) Meas. Sci. Technol., 2, p. 1195
- Malberg, J.H., (1964) Rev. Sci. Instrum., 35, p. 1622
- Bilbao, L., Bruzzone, H., Kelly, H., Esper, M., (1985) IEEE Trans. Plasma Sci., 13, p. 202
- Linz, P., (1985) Analytical and Numerical Methods for Volterra Equations, , SIAM Studies in Applied Mathematics (John Nohel, ed.), Siam, Philadelphia
- Hadamard, J., (1904) Bull. Princeton University, 13, p. 82. , See also P. Garabedian, in: Partial Differential Equations, Wiley, New York 1964, p. 109
- Weyl, F., (1954) Analysis of Optical Methods, in: Physical Measurements in Gas Dynamics and Combustion, 9, p. 15. , High Speed Aerodynamics and Jet Propulsion, Princeton University Press, Princeton, New Jersey
- Fleurier, C., Chapelle, J., (1974) Comput. Phys. Commun., 7, p. 200
- Bockasten, K., (1961) J. Opt. Soc. Amer., 51, p. 943
- Pretzler, G., Jäger, H., Neger, T., Philipp, H., Woisetschläger, J., (1992) Z. Naturforsch, 47 a, p. 955
- Alpert, P., (1981) Journal of Computational Physics, 44, p. 212
Citas:
---------- APA ----------
Bilbao, L.E. & Grondona, D.E.
(1993)
. Inversion of First Kind Volterra Equations: Back to Direct Methods?. Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, 48(11), 1119-1130.
http://dx.doi.org/10.1515/zna-1993-1111---------- CHICAGO ----------
Bilbao, L.E., Grondona, D.E.
"Inversion of First Kind Volterra Equations: Back to Direct Methods?"
. Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences 48, no. 11
(1993) : 1119-1130.
http://dx.doi.org/10.1515/zna-1993-1111---------- MLA ----------
Bilbao, L.E., Grondona, D.E.
"Inversion of First Kind Volterra Equations: Back to Direct Methods?"
. Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, vol. 48, no. 11, 1993, pp. 1119-1130.
http://dx.doi.org/10.1515/zna-1993-1111---------- VANCOUVER ----------
Bilbao, L.E., Grondona, D.E. Inversion of First Kind Volterra Equations: Back to Direct Methods?. Z. Naturforsch. Sect. A J. Phys. Sci. 1993;48(11):1119-1130.
http://dx.doi.org/10.1515/zna-1993-1111