Abstract
An algorithm is developed which computes strict approximations in subspaces of spline functions of degree m − 1 with k fixed knots. The strict approximation is a unique best Chebyshev approximation for a problem defined on a finite set which can be considered as the “best” of the best approximations. Moreover, a sequence of strict approximations defined on certain subsets of an interval I converges to a best approximation on I if k ⩽ m and at least to a nearly best approximation on I if k > m.
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