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Osculatory interpolation


Author: S. W. Kahng
Journal: Math. Comp. 23 (1969), 621-629
MSC: Primary 65.20
DOI: https://doi.org/10.1090/S0025-5718-1969-0247732-7
MathSciNet review: 0247732
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Abstract | References | Similar Articles | Additional Information

Abstract: An explicit method of osculatory interpolation with a function of the form

$\displaystyle R(x) =$ $\displaystyle {f_{00}}({a_0}_0 + {g_0}(x){f_0}_1({a_0}_1 + {g_0}(x){f_0}_2({a_0}_2 + \cdots + {g_0}(x)$    
  $\displaystyle \cdot f_{0, m_0}(a_{0, m_0} + g_0(x)f_{10}(a_{10} + g_1(x)f_{11}(a_{11}$    
  $\displaystyle + \cdots + g_1(x)f_{1,m_1}(a_{1,m_1} + g_1(x)f_{20}(a_{20} + \cdots + {g_{n - 1}}(x)$    
  $\displaystyle \cdot f_{n0}(a_{n0} + g_n(x)f_{n1}(a_{n1} + \cdots + g_n(x)f_{n, m_n}(a_{n,m_n})) \cdots )$    

is described. Error terms for the interpolation are determined.

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

  • [1] S. W. Kahng, Generalized Newton's Interpolation Functions and Their Applications to Chebyshev Approximations, Lockheed Electronics Company Report, 1967.
  • [2] F. M. Larkin, "Some techniques for rational interpolation," Comput. J., v. 10, 1967, pp. 178-187. MR 35 #6334. MR 0215493 (35:6334)
  • [3] A. Ralston, A First Course in Numerical Analysis, McGraw-Hill, New York, 1965, p. 62, 74. MR 32 #8479. MR 0191070 (32:8479)
  • [4] H. E. Salzer, "Note on osculatory rational interpolation," Math. Comp., v. 16, 1962, pp. 486-491. MR 26 #7133. MR 0149648 (26:7133)
  • [5] H. C. Thacher, Jr., "A recursive algorithm for rational osculatory interpolation," SIAM Rev., v. 3, 1961, p. 359.
  • [6] B. Wendropf, Theoretical Numerical Analysis, Academic Press, New York, 1966. MR 33 #5080. MR 0196896 (33:5080)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0247732-7
Article copyright: © Copyright 1969 American Mathematical Society

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