Pitfalls in the Numerical Solution of Linear Ill-Posed Problems - Varah, J. M. (SIAM journal on scientific and statistical computing, 1983)
Very special computational difficulties arise when we attempt to solve linear systems arising from integral equations of the first kind. We examine here existence and uniqueness questions associated with so-called reasonable solutions for such problems, and present results using the best-known methods on inverse Laplace transform problems. We also discuss the choice of free parameters occurring in these methods from the same point of view.