Error bounds for spline and L-spline interpolation
1972; Elsevier BV; Volume: 6; Issue: 1 Linguagem: Inglês
10.1016/0021-9045(72)90079-2
ISSN1096-0430
AutoresBlair Swartz, Richard S. Varga,
Tópico(s)Advanced Numerical Analysis Techniques
ResumoOne of our basic aims here is to obtain improved error bounds for spline and L-spline interpolation at knots, and to obtain certain stability (or perturbation) results for such forms of interpolation. To give a concrete example to illustrate our aim, consider for simplicity the interpolation of a given function f defined on [a, b] by a smooth cubic spline s over a uniform partition A, of [a, b]. Normally, if f E Cl[u, b], then its unique cubic spline interpolant s is defined by
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