BIT Numerical Mathematics

, Volume 13, Issue 2, pp 177–180 | Cite as

Explicit forms for certain Hermite approximations

  • G. M. Phillips


The Hermite polynomial approximation in which function values and the first few derivatives of a given function are matched at two points is given in an explicit form and an error term is deduced. These results are extended to two dimensions.


Error Term Computational Mathematic Explicit Form Polynomial Approximation Hermite Approximation 
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  1. 1.
    G. Birkhoff, M. H. Schultz and R. S. Varga,Piecewise Hermite interpolation in one and two variables with applications to partial differential equations, Numerische Mathematik 11 (1968), 232–256.Google Scholar
  2. 2.
    P. J. Davis,Interpolation and Approximation, Blaisdell, New York (1963).Google Scholar
  3. 3.
    D. D. Stancu,The remainder of certain linear approximation formulas in two variables, J. SIAM Series B Numerical Analysis 1 (1964), 137–163.CrossRefGoogle Scholar

Copyright information

© BIT Foundations 1973

Authors and Affiliations

  • G. M. Phillips
    • 1
  1. 1.Department of Applied MathematicsUniversity of St. AndrewsSt. AndrewsScotland

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