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On a method of Carasso and Laurent for constructing interpolating splines


Authors: M. J. Munteanu and L. L. Schumaker
Journal: Math. Comp. 27 (1973), 317-325
MSC: Primary 65D05
DOI: https://doi.org/10.1090/S0025-5718-1973-0329194-5
MathSciNet review: 0329194
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Abstract: Carasso and Laurent studied a method for computing natural polynomial splines interpolating simple data. We discuss several similar methods which can be applied to numerical construction of more general interpolating splines, including Lg-splines interpolating Extended-Hermite-Birkhoff data.


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

  • [1] P. M. Anselone & P. J. Laurent, "A general method for the construction of interpolating or smoothing spline-functions," Numer. Math., v. 12, 1968, pp. 66-82. MR 40 #3145. MR 0249904 (40:3145)
  • [2] G. D. Byrne & D. N. H. Chi, "Linear multistep formulas based on g-splines," SIAM J. Numer. Anal., v. 9, 1972, pp. 316-324. MR 0311111 (46:10207)
  • [3] C. Carasso & P. J. Laurent, On the Numerical Construction and the Practical Use of Interpolating Spline-Functions, Proc. IFIP Congress Information Processing 68 (Edinburgh, 1968), vol. 1, Mathematics, Software, North-Holland, Amsterdam, 1969, pp. 86-89. MR 40 #8219. MR 0255012 (40:8219)
  • [4] P. J. Davis, Interpolation and Approximation, Blaisdell, Waltham, Mass., 1963. MR 28 #393. MR 0157156 (28:393)
  • [5 C] de Boor, "On calculating with B-splines," J. Approximation Theory, v. 6, 1972, pp. 50-62. MR 0338617 (49:3381)
  • [6] M. Golomb, Spline Approximations to the Solutions of Two-Point Boundary-Value Problems, MRC 1066, Univ. of Wisconsin, Madison, Wis., 1970.
  • [7] T. N. E. Greville, Introduction to Spline Functions, Proc. Sem. Theory of Applications of Spline Functions (Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1968), Academic Press, New York, 1969, pp. 1-35. MR 39 #1868. MR 0240521 (39:1868)
  • [8] J. W. Jerome & L. L. Schumaker, "On Lg-splines," J. Approximation Theory, v. 2, 1969, pp. 29-49. MR 39 #3201. MR 0241864 (39:3201)
  • [9] J. W. Jerome & L. L. Schumaker, "Local bases and computation of g-splines," Methoden und Verfahren der Mathematische Physik, v. 5, 1971, pp. 171-199. MR 0362835 (50:15273)
  • [10] S. Karlin, "Best quadrature formulas and splines," J. Approximation Theory, v. 4, 1971, pp. 59-90. MR 43 #2403. MR 0276661 (43:2403)
  • [11] T. Lyche & L. L. Schumaker, "Computation of smoothing and interpolating natural splines via local bases," SIAM J. Numer. Anal. (To appear.) MR 0336959 (49:1732)
  • [12] M. J. Munteanu, Contributions à la Théorie des Fonctions Splines à une et à Plusieurs Variables, Dissertation, Louvain, 1970.
  • [13] I. J. Schoenberg, "On the Ahlberg-Nilson extension of spline interpolation: the g-splines and their optimal properties," J. Math. Anal. Appl., v. 21, 1968, pp. 207-231. MR 36 #6849. MR 0223802 (36:6849)
  • [14] M. H. Schultz & R. S. Varga, "L-splines," Numer. Math., v. 10, 1967, pp. 345-369. MR 37 #665. MR 0225068 (37:665)
  • [15] L. L. Schumaker, Some Algorithms for the Computation of Interpolating and Approximating Spline Functions, Proc. Sem. Theory and Applications of Spline Functions (Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1968), Academic Press, New York, 1969, pp. 87-102. MR 39 #687. MR 0239330 (39:687)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0329194-5
Article copyright: © Copyright 1973 American Mathematical Society

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