Low degree rational spline interpolation

For a strictly monotone functionf on [a,b] we describe the possibility of finding an interpolating rational splineS of the formS(x)=c0+c1x/(1+d1x) on each subinterval of the grida=x0<x1<...<xn=b. This leads to a nonlinear system for which we get the local existence and uniqueness of a solution. We prove that ‖S−f‖∞=O(h3). Numerical test shows good approximation properties of these splines.