Odd-Degree Spline Interpolation at a Biinfinite Knot Sequence.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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It is shown that for an arbitrary strictly increasing knot sequence t t sub 1 infinity to minus infinity and for every i, there exists exactly one fundamental spline L sub i i.e., L sub it sub j delta sub ij, all j, of order 2r whose r-th derivative is square integrable. Further, Lr sub i x is shown to decay exponentially as x moves away from t sub i, at a rate which can be bounded in terms of r alone. This allows one to bound odd-degree spline interpolation at knots on bounded functions in terms of the global mesh ratio M Sub t sup sub i, j Delta t sub iDelta t sub j. A very nice result of Demkos concerning the exponential decay away from the diagonal of the inverse of a band matrix is slightly refined and generalized to biinfinite matrices.
- Theoretical Mathematics
- Operations Research