Abstract
We consider interpolation of multivariate functions by algebraic polynomials in ℝS, s ≥ 2. Since our methods and results do not depend on dimension s ≥ 2, we restrict ourselves to bivariate interpolation, s=2. Using methods of Birkhoff interpolation from.
Keywords
- Interpolation Problem
- Lagrange Interpolation
- Algebraic Polynomial
- Interpolation Matrix
- Multivariate Interpolation
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Supported in part by NSF Grant MCS8303353.
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References
K. C. Chung and T. H. Yao, On lattices admitting unique Lagrange interpolations, SIAM J. Numer. Anal. 14 (1977), 735–743.
Ciarlet, P.G., The finite element method for elliptic problems, North Holland, New York, 1978.
H. A. Hakopian, Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type, J. Approximation Theory 34 (1982), 286–305.
H. Hakopian, Multivariate spline functions, B-spline basis and polynomial interpolations, SIAM J. Numer. Anal. 19 (1982), 510–517.
S. Karlin and J. M. Karon, Poised and non-poised Hermite-Birkhoff interpolation, Indiana Univ. Math. J. 21 (1972), 1131–1170.
P. Kergin, A natural interpolation of CK functions, J. Approximation Theory 29 (1980), 278–293.
G. G. Lorentz, K. Jetter and S. D. Riemenschneider, Birkhoff Interpolation, Encyclopedia of Mathematics and its Applications, vol. 19, Addison-Wesley, Reading, 1983.
G. G. Lorentz and K. L. Zeller, Birkhoff interpolation problem: coalescence of row, Arch. Math. 26 (1975), 189–192.
C. A. Micchelli, A constructive approach to Kergin interpolation in RK: Multivariate B-splines and Lagrange interpolation, Rocky Mountain J. Math. 10 (1980), 485–497.
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© 1984 Springer-Verlag
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Lorentz, G.G., Lorentz, R.A. (1984). Multivariate interpolation. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072406
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DOI: https://doi.org/10.1007/BFb0072406
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13899-0
Online ISBN: 978-3-540-39113-5
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