A remainder formula and limits of cardinal spline interpolants

Authors:
T. N. T. Goodman and S. L. Lee

Journal:
Trans. Amer. Math. Soc. **271** (1982), 469-483

MSC:
Primary 41A15

DOI:
https://doi.org/10.1090/S0002-9947-1982-0654845-7

MathSciNet review:
654845

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Abstract | References | Similar Articles | Additional Information

Abstract: A Peano-type remainder formula

**[1]**Alfred S. Cavaretta Jr.,*On cardinal perfect splines of least sup-norm on the real axis*, J. Approximation Theory**8**(1973), 285–303. Collection of articles dedicated to Isaac Jacob Schoenberg on his 70th birthday, IV. MR**0350263****[2]**Carl de Boor and I. J. Schoenberg,*Cardinal interpolation and spline functions. VIII. The Budan-Fourier theorem for splines and applications*, Spline functions (Proc. Internat. Sympos., Karlsruhe, 1975) Springer, Berlin, 1976, pp. 1–79. Lecture Notes in Math., Vol. 501. MR**0493059****[3]**Philip J. Davis,*Interpolation and approximation*, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR**0157156****[4]**T. N. T. Goodman,*Necessary conditions for the convergence of cardinal Hermite splines as their degree tends to infinity*, Trans. Amer. Math. Soc.**255**(1979), 231–241. MR**542878**, https://doi.org/10.1090/S0002-9947-1979-0542878-0**[5]**T. N. T. Goodman and S. L. Lee,*The Budan-Fourier theorem and Hermite-Birkhoff spline interpolation*, Trans. Amer. Math. Soc.**271**(1982), no. 2, 451–467. MR**654844**, https://doi.org/10.1090/S0002-9947-1982-0654844-5**[6]**M. J. Marsden and S. D. Riemenschneider,*Cardinal Hermite spline interpolation: convergence as the degree tends to infinity*, Trans. Amer. Math. Soc.**235**(1978), 221–244. MR**0463752**, https://doi.org/10.1090/S0002-9947-1978-0463752-3**[7]**Charles A. Micchelli,*Oscillation matrices and cardinal spline interpolation*, Studies in spline functions and approximation theory, Academic Press, New York, 1976, pp. 163–201. MR**0481735****[8]**F. B. Richards and I. J. Schoenberg,*Notes on spline functions. IV. A cardinal spline analogue of the theorem of the brothers Markov*, Israel J. Math.**16**(1973), 94–102. MR**0425439**, https://doi.org/10.1007/BF02761974**[9]**I. J. Schoenberg,*Notes on spline functions. III. On the convergence of the interpolating cardinal splines as their degree tends to infinity*, Israel J. Math.**16**(1973), 87–93. MR**0425438**, https://doi.org/10.1007/BF02761973**[10]**I. J. Schoenberg,*On the remainders and the convergence of cardinal spline interpolation for almost periodic functions*, Studies in spline functions and approximation theory, Academic Press, New York, 1976, pp. 277–303. MR**0481739**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0654845-7

Article copyright:
© Copyright 1982
American Mathematical Society