Regularization of a discrete backward problem using coefficients of truncated Lagrange polynomials

Abstract

We consider the problem of finding the initial temperature u(x, 0), from a countable set of measured values { u(xj, 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.