Advertisement

Multivariate spline and its applications in science and technology

  • Ren-Hong Wang
Article

Keywords

Algebraic Curve Algebraic Curf Interior Vertex Interior Edge Singular Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. Alfeld, B. Piper, L.L. Schumaker, SIAM, J. Numer. Anal., Vol. 24, No. 4 (1987), pp. 891–911.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    P. Alfeld, B. Piper, L.L. Schumaker, CAGD, 4(1987), pp. 105–123.MATHMathSciNetGoogle Scholar
  3. [3]
    L.J. Billera, Trans. Amer. Math. Soc., 310(1988), pp. 325–340.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    L.J. Billera, L.L. Rose, Discrete Comp. Geom., 6(1991), pp. 107–128.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Y.S. Chui, L.Y. Su, R.H. WangIn Multivariate Approx. Theorey III, Birkhauser Basel, 1985, pp. 71–83Google Scholar
  6. [6]
    Y.S. Chui, T.X. He, R.H. Wang, Coll. Math. Soc. J. Bolyai 49, 1985.Google Scholar
  7. [7]
    Y.S. Chui, R.H. Wang, J. Math. Anal. Appl., 92(1983), pp. 533–551.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Y.S. Chui, R.H. Wang, ibid, J. Math. Anal. Appl., 101 (1984).Google Scholar
  9. [9]
    Y.S. Chui, R.H. Wang, Scientia Sinica (A), 27 (1984), pp. 1129–1142.MATHMathSciNetGoogle Scholar
  10. [10]
    G. Farin, Worsey,CAGD, 1987Google Scholar
  11. [11]
    D. Hong, Approx. Theory & Appl., 1(1991), pp. 56–75Google Scholar
  12. [12]
    Z.X. LuoResearch on non-linear spline functions, Ph.D. Thesis, Dalian Univ. of Tech., 1991Google Scholar
  13. [13]
    Z.X. Luo, R.H. Wang, J. Math. Res. Exposition, 12(1992), pp. 579–582.MATHMathSciNetGoogle Scholar
  14. [14]
    Z.X. Luo, R.H. Wang, J. Dalian Univ. of Tech., 33(1993), pp. 621–627.MATHMathSciNetGoogle Scholar
  15. [15]
    J. Morgan, R. ScottThe dimension of the space of C 1 piecewise polynomials, Unpublished manuscript.Google Scholar
  16. [16]
    J. Morgan, R. Scott, Math. Comp., 29(1975), pp. 736–740.MATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    G. Nürnberg, Th. RiessingerLagrange and Hermite interpolation by bivariate splines, report Univ. of Mannheim, No. 109, 1990.Google Scholar
  18. [18]
    M.J. Powell, M.A. Sabin, ACM Trans. Math. Software., 3(1977), pp. 316–325.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    X.Q. Shi, CAGD, 8(1991), pp. 201–206.MATHGoogle Scholar
  20. [20]
    X.Q. Shi, J. Comp. Math., 10(1992), pp. 224–230.MATHGoogle Scholar
  21. [21]
    X.Q. ShiHigher dimensional splines, Ph.D. Thesis, Jilin Univ., 1988.Google Scholar
  22. [22]
    X.Q. Shi, R.H. WangDecomposition method for studying multivariate splines, J. Math. Res. Exposition, to appear.Google Scholar
  23. [23]
    X.Q. ShiThe, piecewise algebraic curves, Surfaces, and their applications in CAGD, Ph.D. thesis, Dalian Univ. of tech., 1993.Google Scholar
  24. [24]
    R.H. Wang, Acta Math. Sinica, 18(1975), pp. 91–106.MATHMathSciNetGoogle Scholar
  25. [25]
    R.H. Wang, Scientitia Sinica, Math. I(1979), pp. 215–226.Google Scholar
  26. [26]
    R.H. Wang, Numer., Math. J. Chineese Univ., 1(1980), pp. 78–81.Google Scholar
  27. [27]
    R.H. Wang, Proc. Asian Math. Conf. 1990, World Sci. 1992, pp. 474–477.Google Scholar
  28. [28]
    R.H. Wang, Proc. of the 1st China-Japan Seminar on Numer. Math., Aug. 1992, World Sci. 1993, pp. 184–191.Google Scholar
  29. [29]
    R.H. Wang, X.Z. LiangApproximation of multivariate functions, Sci. Press, Beijing, 1988.Google Scholar
  30. [30]
    R.H. Wang, X.G. Lu, Scientitia Sinica (A), 6(1988), pp. 585–594.MathSciNetGoogle Scholar
  31. [31]
    R.H. Wang, X.Y. QianIntersection of two piecewise algebraic curves Google Scholar
  32. [32]
    R.H. Wang, X.Q. ShiA kind of cubic C 1 interpolation in the n-dimensional finite elements method, Res. Report, Inst. of Math., Jilin Univ. 1987; J. Math. Res. Exposition, 1989.Google Scholar
  33. [33]
    R.H. Wang, R. Van DammeCurve interpolation with constrained length, submitted.Google Scholar
  34. [34]
    R.H. Wang, B.Z. YinSequence decomposition method for computing a Gröbner basis and its application in bivariate splines. Submitted.Google Scholar
  35. [35]
    R.H. Wang, Y.W. ZhanOn the C 2 interpolation over Morgan-Scotl split. Submitted.Google Scholar
  36. [36]
    X.S. Wang, Northeastern Math. J., 2(1986), pp. 67–71.Google Scholar
  37. [37]
    P. Zwart, SIAM J. Numer. Anal. (1973).Google Scholar

Copyright information

© Birkhäuser-Verlag 1993

Authors and Affiliations

  • Ren-Hong Wang
    • 1
  1. 1.Dalian University oh TechnologyChina

Personalised recommendations