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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Favard's solution is the limit of $ W\sp{k,p}$-splines


Authors: C. K. Chui, P. W. Smith and J. D. Ward
Journal: Trans. Amer. Math. Soc. 220 (1976), 299-305
MSC: Primary 41A15
MathSciNet review: 0422954
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Abstract: The purpose of this paper is to affirm a conjecture of C. de Boor, namely: The $ {W^{k,p}}$-splines converge in $ {W^{k,r}}[a,b]$ for all $ r,1 \leqslant r < \infty $, to the Favard solution as p tends to infinity.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0422954-0
PII: S 0002-9947(1976)0422954-0
Keywords: Splines, Favard's solution, limit of $ {W^{k,p}}$-splines
Article copyright: © Copyright 1976 American Mathematical Society