Uniform approximation by the highest defect continuous polynomial splines: Necessary and sufficient optimality conditions and their generalisations (Q613594)

The author formulates the problem of polynomial spline approximation as an optimization problem, and then establishes necessary and sufficient optimality conditions for uniform approximation of continuous functions by the highest defect polynomial splines with fixed knots which is a generalization of \textit{Tarashnin}'s theorem [Approximation of the theory of quasidifferentials to solving approximation problems, PhD Thesis, St-Petersburg State University, (1996)]. Necessary and sufficient optimality conditions for polynomial spline approximation with fixed values of the splines at one or both borders of the approximation interval are also derived.