In this paper we consider different regularization methods for solving the heat equation backward in time, where is a linear (unbounded) operator in a Hilbert space with norm and are the available (noisy) data for with . Assuming we consider different regularized solutions for and discuss the question how to choose the regularization parameter in order to obtain optimal estimates sup where the supremum is taken over and .
Cite this article
Ulrich Tautenhahn, T. Schröter, On Optimal Regularization Methods for the Backward Heat Equation. Z. Anal. Anwend. 15 (1996), no. 2, pp. 475–493