Splines (with optimal knots) are better

Abstract

Abstract Let SM k be the Polynominal splines of degree n-1, and with K segments. If f∈ C n [a,b],then the distance in the Lp-norm form(0< p ≦ ∞)of from S M k is boundedby M/K n , with a much smaller M than in similar estimates for other processes of approximation. †This work was supported in part by Air Force contract AF-AFOSR-1206-67. †This work was supported in part by Air Force contract AF-AFOSR-1206-67. Notes †This work was supported in part by Air Force contract AF-AFOSR-1206-67.