Spectral data estimation is an ill-posed problem, since (i) it is difficult to collect sufficient linear independent data and (ii) due to the integral nature of solid-state light sensors, camera outputs do not depend continuously on input signals. To solve these problems, most methods rely on exact a priori knowledge to reduce the problem’s complexity (solution space). In this paper a new algor...

A wavelet regularization approach is presented for dealing with an ill-posed problem of adjoint parameter estimation applied to estimating inflow parameters from down-flow data

Linear equality systems with fuzzy parameters and crisp variables defined by the Zadeh’s extension principle are called possibilistic linear equality systems. This study focuses on the problem of stability (with respect to small changes in the membership function of fuzzy parameters) of the solution in these systems.

Systems Ay ≥ 0 with a degenerate cone of solutions are considered ill-posed since finite-precision algorithms are not expected to find points in the cone of solutions. Consequently, common condition numbers for these systems, such as C(A) [15] and C (A) [2], which are based on the notion of distance to the nearest ill-posed problem, become infinite on such ill-posed instances. In this paper we ...

In this article we investigate the existence of a solution to a semi-linear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one encounters in studying the constraint equations in general relativity. Our method for solving this problem consists of solving a net of regularized, semi-l...