Sommario
In questa nota si descrive un metodo numerico per risolvere il problema generalizzato della «regolarizzazione» dei dati sperimentali quando si usa il funzionale di Schoenberg e di Whittaker; inoltre si stabiliscono alcuni criteri per la determinazione dei «parametri di regolarizzazione». Questo metodo è particolarmente conveniente per risolvere numericamente le equazioni integrali lineari di Fredholm di prima specie.
Abstract
In this paper a numerical method has been developed to solve the generalized problem of smoothing experimental data, when the Scheonberg's and the Whittaker's functionals are considered; some criteria for the determination of the «smoothing parameters» have been established. This method is especially convenient to solve numerically the Fredholm linear integral equations of the first kind.
Bibliografia
I. J. Schoenberg,Spline functions and the problem of graduation. Proc. Nat. Acad. Sci. U.S.A., 52 (1964), 947–950.
E. T. Whittaker,On a new method of graduation. Proc. Edinburgh Math. Soc. 41 (1923), 63–75.
D. L. Phillips,A technique for the numerical solution of certain integral equations of the first kind. Journ. Ass. Comp. Mach. 9 (1962), 84–97.
S. Twomey,On the numerical solution of Fredholm integral equation of the first kind by the inversion of the linear system produced by quadrature. Journ. Ass. Comp. Mach. 10 (1963), 97–101
A. N. Tikhonov,The solution of uncorrectly posed problems and the method of regularization. Dokl. Akad. Nauk SSSR 151 (1963), 501–594.
A. N. Tikhonov,The regularization of incorrectly posed problems. Dokl. Akad. Nauk. SSSR 153 (1963), 42–52.
A. N. Tikhonov, V. B. Glasko,The approximate solution of Fredholm integral equations of the first kind. USSR Comp. Math. e Math. Physics 4 (1964), 236–247.
A. N. Tikhonov, V. B. Glasko,Use of tye regularization method in non linear problems. USSR Comp. Math. e Math. Physics 5 (1965), 93–106.
T. N. E. Greville (editor), Theory and Application of Spline Functions (1969), Academic Press, New York.
P. M. Anselone, P. J. Laurent,A general method for the construction of interpolating or smoothing spline-functions. Numer. Mathem. 12 (1998), 66–82.
C. H. Reinsch,Smoothing by spline functions. Numer. Mathem. 10 (1967), 177–183.
C. H. Reinsch,Smoothing by spline functions II. Numer. Mathem. 16 (1971), 451–454.
J. Riordan,Combinatorial Identities (1968), J. Wiley & Sons, New York.
G. Golub,Numerical methods for solving linear least squares problem. Numer. Mathem. 7 (1965), 206–216.
Procédures Algol en Analyse Numérique (1970), Edit. Centre Nat. Recher. Scient., Paris.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Galligani, I. Sulla «Regolarizzazione» dei dati sperimentali. Calcolo 8, 359–376 (1971). https://doi.org/10.1007/BF02575802
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02575802