Fast one-sided approximation with spline functions (Q1095565)

Using the quadratic spline, the author constructs operators U and L and gives the following main theorem concerning interpolants and one-sided approximation. \(Uf=f=Lf\) for \(f\in P_ 3\). Uf\(\geq f\geq Lf\) for \(f\in P_ 4\). \(Uf_ i\geq f_ i\geq Lf_ i\) for ith knot and for any function f. \(U^ 2\geq U\geq L\geq L^ 2\). \(\| U\|\), \(\| L\| \leq 1+p2/2(1+p)\). \(U(f+g)\leq Uf+Ug\). Here \(P_ n\) is the space of all polynomials with degree n and p is a constant related to the length of subintervals divided by knots.