Maximum entropy method for solving operator equations of the first kind (Q1368261)

For finding the nonnegative solution to the first-kind linear operator equation with approximately known right-hand side and operator, the authors consider the maximum entropy method at which unlike the Tikhonov regularization a nonquadratic optimization problem is solved. They study the maximum entropy method by different approaches and obtain stability and convergence results. Under the ``source condition'' suitable rates of convergence are derived and an a posteriori choice for the regularization parameter is proposed.