Geodesic
Regularization of a discrete backward problem using coefficients of truncated Lagrange polynomials
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider the problem of finding the initial temperature $u(x,0)$, from a countable set of measured values $\{ u(x_j,1)\}$. The problem is severely ill-posed and a regularization is in order. Using the Hermite polynomials and coefficients of truncated Lagrange polynomials, we shall change the problem into an analytic interpolation problem and give explicitly a stable approximation. Error estimates and some numerical examples are given.
Classification : 30E05, 33C45, 35K05
Keywords: discrete backward problem, truncated Lagrange polynomial, Hermite polynomial, interpolation problem 
@article{EJDE_2007__2007__a160,
     author = {Dang Duc Trong and Tran Ngoc Lien},
     title = {Regularization of a discrete backward problem using coefficients of truncated {Lagrange} polynomials},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a160/}
}
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Dang Duc Trong; Tran Ngoc Lien. Regularization of a discrete backward problem using coefficients of truncated Lagrange polynomials. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a160/