We study weighted total least squares problems on infinite dimensional spaces. We present some necessary and sufficient conditions for the regularized problem to have a solution. The existence of solution can also be assured ...

The indefinite least-squares problem has been thoroughly studied before under the assumption that the range of C is a uniformly J-positive subspace of K. Along this article the range of C is only supposed to be a J-nonnegative ...

The kernel regularized least squares (KRLS) method uses the kernel trick to perform non-linear regression estimation. Its performance depends on proper selection of both a kernel function and a regularization parameter. ...

Minimum residual methods such as the least-squares finite element method (FEM) or the discontinuous Petrov-Galerkin (DPG) method with optimal test functions usually exclude singular data, e.g., non-square-integrable loads. ...

We study variants of the mixed finite element method (mixed FEM) and the first-order system least-squares finite element (FOSLS) for the Poisson problem where we replace the load by a suitable regularization which permits ...

We study variants of the mixed finite element method (mixed FEM) and the first-order system least-squares finite element (FOSLS) for the Poisson problem where we replace the load by a suitable regularization which permits ...