Splines with nonnegative spline coefficients
Authors:
C. de Boor and James W. Daniel
Journal:
Math. Comp. 28 (1974), 565568
MSC:
Primary 65D15
MathSciNet review:
0378357
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Abstract: We consider the question of the approximation of nonnegative functions by nonnegative splines of order k (degree ) compared with approximation by that subclass of nonnegative splines of order k consisting of all those whose Bspline coefficients are nonnegative; while approximation by the former gives errors of order , the latter may yield only . These results are related to certain facts about quasiinterpolants.
 [1]
C. de Boor, "On uniform approximation by splines," J. Approximation Theory, v. 1, 1968, pp. 219235. MR 39 #1866. MR 0240519 (39:1866)
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C. de Boor & G. J. Fix, "Spline approximation by quasiinterpolants," J. Approximation Theory, v. 8, 1973, pp. 1945. MR 0340893 (49:5643)
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H. Burchard, "Extremal positive splines with applications to interpolation and approximation by geheralized convex functions," Symposium on Approximation Theory, University of Texas, Austin, Texas, 1973. MR 0338620 (49:3384)
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H. B. Curry & I. J. Schoenberg, "On Polya frequency functions. IV: The fundamental spline functions and their limits," J. Analyse Math., v. 17, 1966, pp. 71107. MR 36 #1884. MR 0218800 (36:1884)
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M. J. Marsden, "An identity for spline functions with applications to variationdiminishing spline approximation," J. Approximation Theory, v. 3, 1970, pp. 749. MR 40 #7682. MR 0254474 (40:7682)
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I. J. Schoenberg, "On spline functions," in Inequalities, (Proc. Sympos. WrightPatterson Air Force Base, Ohio, 1965), Academic Press, New York, 1967, pp. 255291. MR 36 #6848. MR 0223801 (36:6848)
 [1]
 C. de Boor, "On uniform approximation by splines," J. Approximation Theory, v. 1, 1968, pp. 219235. MR 39 #1866. MR 0240519 (39:1866)
 [2]
 C. de Boor & G. J. Fix, "Spline approximation by quasiinterpolants," J. Approximation Theory, v. 8, 1973, pp. 1945. MR 0340893 (49:5643)
 [3]
 H. Burchard, "Extremal positive splines with applications to interpolation and approximation by geheralized convex functions," Symposium on Approximation Theory, University of Texas, Austin, Texas, 1973. MR 0338620 (49:3384)
 [4]
 H. B. Curry & I. J. Schoenberg, "On Polya frequency functions. IV: The fundamental spline functions and their limits," J. Analyse Math., v. 17, 1966, pp. 71107. MR 36 #1884. MR 0218800 (36:1884)
 [5]
 M. J. Marsden, "An identity for spline functions with applications to variationdiminishing spline approximation," J. Approximation Theory, v. 3, 1970, pp. 749. MR 40 #7682. MR 0254474 (40:7682)
 [6]
 I. J. Schoenberg, "On spline functions," in Inequalities, (Proc. Sympos. WrightPatterson Air Force Base, Ohio, 1965), Academic Press, New York, 1967, pp. 255291. MR 36 #6848. MR 0223801 (36:6848)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403783572
PII:
S 00255718(1974)03783572
Keywords:
Nonnegative splines,
onesided approximation,
splines,
approximation
Article copyright:
© Copyright 1974
American Mathematical Society
