Showing papers by "Patricia J. Y. Wong published in 1994"
TL;DR: In this article, the authors provided explicit error estimates between a given function x ∈ PC ( n ) [a, b ], 2 ≤ n ≤ 6 and its quintic spline interpolate S Δ x ( t ).
Abstract: The purpose of this paper is to provide explicit error estimates between a given function x ( t ∈ PC ( n ) [ a, b ], 2 ≤ n ≤ 6 and its quintic spline interpolate S Δ x ( t ). The results obtained are sharp and improve on, or supplement, those established by Hall [1] and Schultz [2]. These results are then used to acquire precise error bounds for the approximated and biquintic spline interpolates. Sufficient numerical illustration which dwells upon the importance of the obtained results is also included.
28 citations
TL;DR: In this article, the authors derived explicit error estimates in L ∞ norm between a given function f ( x ) ∈ PC ( n ) [a, b ], 4 ≤ n ≤ 6 and its quintic Lidstone-spline interpolate.
Abstract: In this paper, we shall derive explicit error estimates in L ∞ norm between a given function f ( x ) ∈ PC ( n ) [ a , b ], 4 ≤ n ≤ 6 and its quintic Lidstone-spline interpolate. The results obtained are then used to establish precise error bounds for the approximated and biquintic Lidstone-spline interpolates. We also include applications to integral equations and boundary value problems as well as sufficient numerical examples which dwell upon the sharpness of the obtained results.
10 citations
TL;DR: In this article, the authors provide explicit error bounds for spline interpolation in L 2 -norms, and extend these bounds to cases not considered by Schultz [19] and [20].
Abstract: The purpose of this paper is to provide explicit error bounds for the derivatives of spline interpolation in L2– norm. These bounds not only correct but also improve on those given by Schultz [19], and extend to cases not considered by him.
6 citations
TL;DR: In this paper, the authors provide explicit error bounds for derivatives of piecewise-Hermite interpolates in L"2-norm, and extend these bounds to cases not considered by Schultz.
3 citations