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Closed-form Representations for Errors of Cubic Spline Approximations on Equally Spaced Knots

Authors:	RIESS, R. D. JOHNSON, L. W.

Affiliation:	Department of Mathematics, Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061, U.S.A.

Abstract:	This paper considers estimating errors in the approximationof an arbitrary linear functional on C⁴[0, L] by use of cubicsplines on equally spaced knots. Using explicit formulas derivedfor the cubic spline approximations of f_k(x) = cos (k ${pi}$ x/L), formulasare found for the cosine expansion of the Peano Kernel for theremainder functional.

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