Error bounds for polynomial spline interpolation
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- by Martin H. Schultz PDF
- Math. Comp. 24 (1970), 507-515 Request permission
Abstract:
New upper and lower bounds for the ${L^2}$ and ${L^\infty }$ norms of derivatives of the error in polynomial spline interpolation are derived. These results improve corresponding results of Ahlberg, Nilson, and Walsh, cf. [1], and Schultz and Varga, cf. [5].References
- J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The theory of splines and their applications, Academic Press, New York-London, 1967. MR 0239327
- Richard Bellman, A note on an inequality of E. Schmidt, Bull. Amer. Math. Soc. 50 (1944), 734–736. MR 10732, DOI 10.1090/S0002-9904-1944-08228-1
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, New York-Chicago, Ill.-Toronto, Ont., 1966. MR 0213785
- M. H. Schultz and R. S. Varga, $L$-splines, Numer. Math. 10 (1967), 345–369. MR 225068, DOI 10.1007/BF02162033
- Survey of numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR 0135221
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Math. Comp. 24 (1970), 507-515
- MSC: Primary 41.30; Secondary 65.00
- DOI: https://doi.org/10.1090/S0025-5718-1970-0275025-9
- MathSciNet review: 0275025