Best \(L_ 1\)-approximation
This paper studies best \(L_ 1\)-approximation of continuous functions defined on an interval [a,b]. First a condition is established ensuring uniqueness of best \(L_ 1\)-approximation. This condition can be considered as a generalized Haar condition. Using it, a short proof of uniqueness of best \(L_ 1\)-approximation from subspaces of spline functions is given. Then the relationship between best \(L_ 1\)- approximation and certain classes of perfect splines is considered. These results can be applied to construct bounds for the error of best \(L_ 1\)-approximations from spline subspaces. These estimates have an application in numerical integration.
scientific article; zbMATH DE number 3863800