ON THE Relationship between Functions with the Same Optimal Knots in Spline with Piecewise Polynomial Approximation.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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The relationship between functions with the same optimal knows for L sub 2 0,1 approximation by k-th order splines or piecewise polynomials is investigated. It is shown that, if two functions have positive continuous k-th derivatives, they will have the same optimal knots if and only if they differ by a polynomial of order k. An application to design selection for continuous time regression is considered and extensions to L sub p approximation are also provided. Author
- Theoretical Mathematics