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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Osculatory interpolation

Author: S. W. Kahng
Journal: Math. Comp. 23 (1969), 621-629
MSC: Primary 65.20
MathSciNet review: 0247732
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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.

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Article copyright: © Copyright 1969 American Mathematical Society

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