Osculatory interpolation

Kahng, S. W.

doi:10.1090/S0025-5718-1969-0247732-7

Osculatory interpolation
HTML articles powered by AMS MathViewer

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

Generalized Newton’s Interpolation Functions and Their Applications to Chebyshev Approximations

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

SIAM Rev.

Burton Wendroff, Theoretical numerical analysis, Academic Press, New York-London, 1966. MR 0196896