An algorithm for the computation of strict approximations in subspaces of spline functions (Q796006)

In this paper best Chebyshev approximations of continuous functions f from subspaces of spline functions \(S_{m-1,k}\) of degree m-1 with k fixed knots are studied. An algorithm is developed which computes strict approximations. The strict approximation is a unique best Chebyshev approximation for a problem defined on a finite set. This approximation can be considered as the ''best'' of the best approximations. Then a Remez type algorithm for an approximation problem defined on the interval I is defined. Sequences of strict approximations from \(S_{m-1,k}\) to a given function f on certain finite subsets of I are considered. These sequences converge to a best approximation of f from \(S_{m-1,k}\) on I if \(k\leq m\) and at least to a nearly best approximation on I if \(k>m\).