Least squares approximation and extremal properties (Q2895240)

This paper deals with best approximation in semi-inner product spaces \(H\) where functions of \(H\) are approximated in the underlying semi-norm by functions of a finite dimensional subspace \(U\). The approximation problems are transformed to quadratic optimization problems. The different regularization terms are used in these approximation problems. The solutions of these best approximations satisfy important extremal properties. The main purpose of the paper is to study such extremal properties. Some results of the paper are well-known. The new results are applied to some special problems. The examples show the meaning of the new results.