The training of some types of neural networks leads to separable non-linear least squares problems. These problems may be ill-conditioned and require special techniques. A robust algorithm based on the Variable Projections method of Golub and Pereyra is designed for a class of feed-forward...

We consider the solution of elliptic problems in general regions by embedding and least squares approximation of overdetermined collocated tensor product of basis functions. The resulting least squares problem will generally be ill-conditioned or even singular, and thus, regularization...