Cubic Fitting Splines for Constructing Smooth Curves

Abstract

For a given function f ∈ C[a,b], we assume that the ordinates $u_i \approx f(x_i )$ are known approximately for n + 1 nodes x _i ∈ [a,b]. If the u _i are obtained by measurements which are in general imprecise, the deviations in the data u _i render a straightforward approximation using interpolating methods meaningless. Instead, one needs to find an error compensating function S whose graph passes near the interpolation points (x _i , u _i ) and is as smooth as possible.