Unicity of best mean approximation by second order splines with variable knots Academic Article uri icon


  • Let S N 2 S_N^2 denote the nonlinear manifold of second order splines defined on [0, 1] having at most N N interior knots, counting multiplicities. We consider the ques tion of unicity of best approximations to a function f f by elements of S N 2 S_N^2 . Approximation relative to the L 2 [ 0 , 1 ] {L_2}[0,1] norm is treated first, with the results then extended to the best L 1 {L_1} and best one-sided L 1 {L_1} approximation problems. The conclusions in each case are essentially the same, and can be summarized as follows: a sufficiently smooth function f f satisfying f > 0 f > 0 has a unique best approximant from S N 2 S_N^2 provided either log f log f is concave, or N N is sufficiently large, N N 0 ( f ) N geqslant {N_0}(f) ; for any N

published proceedings

  • Mathematics of Computation

author list (cited authors)

  • Barrow, D. L., Chui, C. K., Smith, P. W., & Ward, J. D.

citation count

  • 18

complete list of authors

  • Barrow, DL||Chui, CK||Smith, PW||Ward, JD

publication date

  • January 1978