Least Square Polynomial Spline Approximations

Author: Patent, Paul David

Year: 1972

Degree: Dissertation (Ph.D.)

Advisor: Keller, Herbert Bishop

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/G4VR-YF05

Abstract

Bounds are derived for both the L²- and L^∞-norms of the error in approximating sufficiently smooth functions by polynomial splines using an integral least square technique based on the theory of orthogonal projection in real Hilbert space. Quadrature schemes for the approximate solution of this least square problem are examined and bounds for the error due to the use of such schemes are derived. The question of the consistency of such quadrature schemes with the least square error is investigated and asymptotic results are presented. Numerical results are also included.

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