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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 6
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Original Articles

Some researches on multivariate Lagrange interpolation along the sufficiently intersected algebraic manifold

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Pages 669-685 | Received 20 Oct 2006, Accepted 21 Feb 2007, Published online: 27 Jun 2007

References

  • de Boor , C and Ron , A . 1990 . On multivariate polynomial interpolation . Constructive Approximation , 6 : 287 – 302 .
  • Sauer , T . 1998 . Polynomial Interpolation of Minimal Degree and Gröbner Bases, London Math. Soc , Vol. 251 , 483 – 494 . London : Cambridge University Press . Lecture Note Series
  • Xu , Y . 2000 . Polynomial interpolation in several variables, cubature formulae and ideals . Advances in Computational Mathematics , 12 : 363 – 376 .
  • Radon , J . 1948 . Zur mechanischen kubatur . Monatshefte Mathematik , 52 : 286 – 300 .
  • Liang , XZ . 1965 . On interpolation and approximation of functions in several variables. , Changchun : Jilin University . Master's Degree Thesis
  • Chung , CK and Yao , TH . 1977 . On lattices admitting unique Lagrange interpolations . SIAM Journal on Numerical Analysis , 14 : 735 – 743 .
  • Mysovskikh , IP . 1981 . Interpolatory cubature formulas (in Russian). Izdat. , Moscow, , Leningrad : Nauka .
  • Bos , L . 1991 . On certain configurations of points in Rn which are unisolvent for polynomial interpolation . Journal of Approximation Theory , 64 : 271 – 280 .
  • Liang , XZ , Lü , CM and Feng , RZ . 2001 . Properly posed set of nodes for multivariate Lagrange interpolation in Cs. . SIAM Journal on Numerical Analysis , 39 ( 2 ) : 587 – 597 .
  • Liang , XZ and Lü , CM . 1998 . “ Properly posed set of nodes for bivariate Lagrange interpolation. ” . In Approximation Theory IX, Vol. 2: Computational Aspect , Edited by: Chui , CK and Schumaker , LL . 189 – 196 . Nashville, TN : Vanderbilt University Press .
  • Liang , XZ , Cui , LH and Zhang , JL . 2002 . Properly Posed set of Nodes for Bivariate Lagrange Interpolation Along an Algebraic Curve, Analysis, Combinatorics and Computing , 295 – 304 . NY, , USA : Publishers, Inc. Commack, Nova Science .
  • Liang , XZ , Cui , LH and Zhang , JL . 2004 . The application of Cayley-Bacharach theorem to bivariate Lagrange interpolation. . Journal of Computational and Applied Mathematics , 163 ( 1 ) : 177 – 187 .
  • Liang , XZ , Wang , RH , Cui , LH , Zhang , JL and Zhang , M . 2006 . Some researches on trivariate Lagrange interpolation . Journal of Computational and Applied Mathematics , 195 : 192 – 205 .
  • Wang , RH and Liang , XZ . 1988 . Approximation of Multivariate Function , Beijing : Science Press .
  • Hartshorne , R . 1977 . Algebraic geometry , New York : Springer-Verlag .
  • Macaulay , FS . 1916 . Algebraic Theory of Modular Systems , London : Cambridge University Press .

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