Geodesic
Regularization of a discrete backward problem using coefficients of truncated Lagrange poly\-nomials
Electronic journal of differential equations, Tome 2007 (2007)
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__a60,
     author = {Dang Duc Trong and Tran Ngoc Lien},
     title = {Regularization of a discrete backward problem using coefficients of truncated {Lagrange} poly\-nomials},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1120.30031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a60/}
}
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Dang Duc Trong; Tran Ngoc Lien. Regularization of a discrete backward problem using coefficients of truncated Lagrange poly\-nomials. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a60/