Osculatory interpolation
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- by S. W. Kahng PDF
- Math. Comp. 23 (1969), 621-629 Request permission
Abstract:
An explicit method of osculatory interpolation with a function of the form \begin{align*} R(x) = & {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) \\ & \cdot f_{0, m_0}(a_{0, m_0} + g_0(x)f_{10}(a_{10} + g_1(x)f_{11}(a_{11} \\ & + \cdots + g_1(x)f_{1,m_1}(a_{1,m_1} + g_1(x)f_{20}(a_{20} + \cdots + {g_{n - 1}}(x) \\ & \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 ) \end{align*} is described. Error terms for the interpolation are determined.References
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S. W. Kahng, Generalized Newton’s Interpolation Functions and Their Applications to Chebyshev Approximations, Lockheed Electronics Company Report, 1967.
- F. M. Larkin, Some techniques for rational interpolation, Comput. J. 10 (1967), 178–187. MR 215493, DOI 10.1093/comjnl/10.2.178
- Anthony Ralston, A first course in numerical analysis, McGraw-Hill Book Co., New York-Toronto-London, 1965. MR 0191070
- Herbert E. Salzer, Note on osculatory rational interpolation, Math. Comp. 16 (1962), 486–491. MR 149648, DOI 10.1090/S0025-5718-1962-0149648-7 H. C. Thacher, Jr., "A recursive algorithm for rational osculatory interpolation," SIAM Rev., v. 3, 1961, p. 359.
- Burton Wendroff, Theoretical numerical analysis, Academic Press, New York-London, 1966. MR 0196896
Additional Information
- © Copyright 1969 American Mathematical Society
- 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