ON THE CONSTRUCTION OF SMOOTHING SPLINES BY QUADRATIC PROGRAMMING

Abstract

. The problem of minimization of a smoothing functional under inequality constraints, which has a solution in the form of a natural spline, is reduced to the problem of quadratic programming with a positive semidefinite matrix. Using the results of quadratic programming, we obtain the modified simplex method for the solution of this problem by adding—-removing interpolating knots of a spline.