Polynomial and Spline Approximation by Quadratic Programming The problem of approximation to a given function, or of fitting a given set of data, where the approximating function is required to have certain of its derivations of specified sign over the whole range of approximation, is studied. Two approaches are presented, in each of which quadratic programming is used to provide both the constraints on the derivatives and the selection of the function which yields the best fit. The first is a modified Bernstein polynomial scheme, and the second is a spline fit. CACM July, 1969 Amos, D. E. Slater, M. L. constant sign derivatives, Bernstein polynomials, linear concavity constraints, quadratic programming splines 5.13 5.41 CA690705 JB February 17, 1978 9:22 AM 1875 5 1875 1875 5 1875 1875 5 1875