On the L2 improperly posed problems

A Mollification Framework for Improperly Posed Problems

1. Introduction Various authors have explored the role of molliication in the solution of improperly posed problems such as numerical diierentiation and the numerical solution of rst kind integral equations. For example, Murio 13], exploiting earlier suggestions of Manselli and Miller 11] as well as Vasin 16], has shown how molliied numerical diierentiators can be constructed for the diierentia...

The Finite Element Method in a Family of Improperly Posed Problems

The numerical solution of the Cauchy problem for elliptic equations is considered. We reformulate the original problem as a variational inequality problem, which we solve using the finite element method. Moreover, we prove the convergence of the approximate solution. Let <$> be a bounded open set in the space R" and d6^ be the boundary of fy. Then ßr = ty X (0, T) is a bounded open set in Rn+I....

On Six Problems Posed

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

On Two Problems Posed by Kenneth Stolarsky

Solutions of two slightly more general problems than those posed by Kenneth B. Stolarsky in [10] are presented. The latter deal with a shape preserving approximation, in the uniform norm, of two functions (1/x) log coshx and (1/x) log(sinhx/x), x ≥ 0, by ratios of exponomials. The main mathematical tools employed include Gini means and the Stolarski means.