Smoothest interpolation with boundary conditions in $W^3_2[a,b]$

Abstract

We study the problem on the smoothest interpolant with boundary conditions in the Sobolev space $W^3_2[a,b]$. Characterization and uniqueness of the best interpolant with free knots of interpolation, satisfying boundary conditions, are proved. Based on our proofs we present an algorithm for finding the unique oscillating spline interpolant. Numerical results are given.