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)=c ₀ +c ₁ x/(1+d ₁ x) on each subinterval of the grida=x _{0 1} <... _n =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(h ³). Numerical test shows good approximation properties of these splines.