On the uniqueness of best 𝐿₂[0,1] approximation by piecewise polynomials with variable breakpoints

Abstract

In this paper a sufficient condition for the uniqueness of best L 2 [ 0 , 1 ] {L_2}[0,1] approximation by piecewise polynomials of order k with variable breakpoints is generalized from that of order 2. Other extensions included here are nonuniqueness and eventual uniqueness results.