Spline Regression: Algorithms and Local Dependence.
YALE UNIV NEW HAVEN CONN DEPT OF COMPUTER SCIENCE
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Curve fitting has been an important problem in data analysis and curve design for many years. Spline regression is a relatively new mathematical curve fitting method which has proved to be useful for moderately accurate 2 to 5 decimal digit approximations to data which are difficult to approximate by analytic means. The qualitative behavior of least-squares spline approximations differs significantly from that of most classical approximation schemes in that least-squares splines are highly local. While the value of a polynomial or any other analytic function at a point can be determined from its value and derivatives at any arbitrarily distant point, the value of the least-squares spline at any point is almost completely determined by neighboring data. In this dissertation, a detailed analysis of algorithms for computing and evaluating least-squares spline approximations to data is presented. The algorithms are given explicitly in an ALGOL-like language and operation counts are presented. Of particular interest are a fast incremental algorithm for evaluating splines and a limited-storage algorithm for computing piecewise polynomial representations of splines.
- Statistics and Probability