Least-Squares Fitting of a Polynomial Constrained to be Either Non-Negative, Non-Decreasing or Convex
非负、单调或凸约束下的多项式最小二乘拟合
Summary An algorithm is provided to fit the (unique) least-squares polynomial Y(x) to n data points (x, y) subject to a constraint that it be either non-negative, non-positive, non-decreasing, non-increasing, convex or concave at all points x in a closed interval I. Some generalization to a general linear model can be handled, and certain alternative constraints can also be dealt with. The problem is close to the classical problem of Quadratic Programming (Q.P.), and some of…