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Error bounds for polynomial spline interpolation


Author: Martin H. Schultz
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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  • [2] R. Bellman, "A note on an inequality of E. Schmidt," Bull. Amer. Math. Soc., v. 50, 1944, pp. 734-736. MR 6, 61. MR 0010732 (6:61g)
  • [3] G. H. Hardy, J. E. Littlewood & G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, New York, 1952. MR 13, 727. MR 0046395 (13:727e)
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  • [5] M. H. Schultz & R. S. Varga, "$ L$-splines," Numer. Math., v. 10, 1967, pp. 345-369. MR 37 #665. MR 0225068 (37:665)
  • [6] J. Todd (Editor), A Survey of Numerical Analysis, McGraw-Hill, New York, 1962. MR 24 #B1271. MR 0135221 (24:B1271)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0275025-9
Keywords: Spline, interpolation, approximation
Article copyright: © Copyright 1970 American Mathematical Society

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