On orthogonal linear \(\ell_1\) approximation
By using a special approach to a given data fitting problem the authors arrive at a minimization problem of the following form: minimize \(\| Zv\|_ 1\) subject to \(v\in {\mathbb{R}}^ n\) and \(\| v\|_ 2=1\), where Z is a given \(m\times n\)-matrix. This problem is equivalent to a concave quadratic programming problem. A characterization of local solutions and a result on the stability of these solutions under small perturbations of the matrix Z is given. Moreover, an algorithm for solving the minimization problem is presentd and its convergence to a special solution is shown. Finally, the performance of the algorithm is illustrated by applying the method to some examples known in the literature.
scientific article; zbMATH DE number 4030807
scientific article