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An interpolation by successive derivatives at a finite set
Published online by Cambridge University Press: 17 April 2009
Abstract
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For an n-times differentiable function f(x) whose derivatives f(j)(xj) at x = xj, j = 0, 1, …, n are specified, we introduce a sequence of fundamental polynomials 
to interpolate f(x) with a remainder as
The remainder R(x|x0, x1,… xn) is given in an integral form and Lagrange's form.
In addition, by introducing orthogonality of Sobolev type we verify the best optimality of the approximations and interpret the fundamental polynomials 
as a kind of Sobolev orthogonal polynomial.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 513 - 524
- Copyright
- Copyright © Australian Mathematical Society 1998
References
[1]Davis, P.J., Interpolation and approximation (Blaisdell, New York, Toronto, London, 1963).Google Scholar
[2]Jung, I.H., Kwon, K.H., and Littlejohn, L.L., ‘Sobolev orthogonal polynomials and spectral differential equations’, Trans. Amer. Math. Soc. 347 (1995), p. 3629–3643.CrossRefGoogle Scholar
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