Laguerre polynomials and the inverse Laplace transform using discrete data

Tran Ngoc Lien (1) , Dang Duc Trong (2) , Alain Pham Ngoc Dinh (3)

1 Faculty of Sciences of Cantho
2 UNS-HCMC - University of Natural Sciences HoChiMinh City
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We consider the problem of finding a function defined on $(0,\infty)$ from a countable set of values of its Laplace transform. The problem is severely ill-posed. We shall use the expansion of the function in a series of Laguerre polynomials to convert the problem in an analytic interpolation problem. Then, using the coefficients of Lagrange polynomials we shall construct a stable approximation solution.

Mots clés: Inverse Laplace transform; Laguerre polynomials; Lagrange polynomials; ill-posed problem; regularization.; regularization

Domaines: Equations aux dérivées partielles [math.AP]

Tran Ngoc Lien, Dang Duc Trong, Alain Pham Ngoc Dinh. Laguerre polynomials and the inverse Laplace transform using discrete data. Journal of Mathematical Analysis and Applications, 2008, 337, pp.1302-1314. ⟨hal-00098062v4⟩