Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems (Q2572610)

First the authors briefly study the properties of the solution of: \[ \min w^Tx,\text{ subject to }\| ax-b\| \leq \varepsilon,\;\| x-d\| \leq \delta, \] from the point of view of regularization. Then they summarize the basic algorithm of \textit{L. Eldén} [BIT 30, 466--483 (1990; Zbl 0702.65041)] -- the core of this algorithm is the computation of the smallest root of a special nonlinear function. This is followed by a description of the algorithm for this problem and some implementation issues. Finally, they demonstrate the use of the proposed algorithm for the sideways heat equation problem.