Splines came out of the barrel of a cannon. Papers on what we now call splines had appeared before Schoenberg’s basic spline paper [31*] on techniques for interpolation and smoothing of ballistic tables. Two of the most interesting ones, [Ea] and [QC], even share with [31*] the subject matter, namely cardinal spline interpolation, and approach it in the same way, namely with the aid of the Fourier transform. [31*] is nevertheless the foundation of spline theory since it is the first paper which treats smooth piecewise polynomials not just as useful auxiliary constructs but as objects deserving of study in their own right, in token of which it provided them with a name, splines. More than that, [31*] bases its analysis of splines on that most useful of spline functions, the B-spline, which is introduced there in terms of its Fourier transform.
KeywordsSpline Space Spline Interpolant Cardinal Spline Ballistic Table Spline Theory
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