On Hm,∞-Splines

Charles K. Chui; Philip W. Smith

doi:10.1137/0711047

On H^m,∞-Splines

Charles K. Chui
, Philip W. Smith

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

4 Citations (Scopus)

61 Downloads (Pure)

Abstract

In this paper, we show that the H^m,∞-splines obtained by taking the limits of the H^m,p-splines, as p=p_n→∞, are unique for certain data. In particular, when Hermite data is specified, the H^m,p-splines converge to a unique H^m,∞-spline in H^m,2. This method enables us to calculate the “natural” Hermite H^2,∞-splines explicitly.

Original language	English
Pages (from-to)	554-558
Number of pages	5
Journal	SIAM Journal on Numerical Analysis
Volume	11
Issue number	3
DOIs	https://doi.org/10.1137/0711047
Publication status	Published - May 1974

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title = "On Hm,∞-Splines",

abstract = "In this paper, we show that the Hm,∞-splines obtained by taking the limits of the Hm,p-splines, as p=pn→∞, are unique for certain data. In particular, when Hermite data is specified, the Hm,p-splines converge to a unique Hm,∞-spline in Hm,2. This method enables us to calculate the “natural” Hermite H2,∞-splines explicitly.",

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AU - Smith, Philip W.

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N2 - In this paper, we show that the Hm,∞-splines obtained by taking the limits of the Hm,p-splines, as p=pn→∞, are unique for certain data. In particular, when Hermite data is specified, the Hm,p-splines converge to a unique Hm,∞-spline in Hm,2. This method enables us to calculate the “natural” Hermite H2,∞-splines explicitly.

AB - In this paper, we show that the Hm,∞-splines obtained by taking the limits of the Hm,p-splines, as p=pn→∞, are unique for certain data. In particular, when Hermite data is specified, the Hm,p-splines converge to a unique Hm,∞-spline in Hm,2. This method enables us to calculate the “natural” Hermite H2,∞-splines explicitly.

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DO - 10.1137/0711047

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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 3

ER -

On H^m,∞-Splines

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