Characterization of strict approximations in subspaces of spline functions (Q796007)

In this paper the problem of approximating a given function f in C(T) by a subspace of spline functions of degree m-1 with k fixed knots where T is a compact subset of \({\mathbb{R}}\) is considered. One of the difficulties lies in the fact that the best approximation is not always unique. Rice defined a ''strict approximation'' which is a uniquely determined best approximation for approximation problems defined on a finite set. First strict approximations from subspaces of spline functions are characterized for problems on finite sets. Then approximation problems defined on an interval are studied. For a great class of continuous functions uniquely determined best approximations are defined which can be considered as strict approximations.