메뉴 건너뛰기




Volumn 119, Issue 1-2, 2000, Pages 347-376

Interpolation by spline spaces on classes of triangulations

Author keywords

41A05; 41A15; 41A63; 65D05; 65D07; 65D17; B zier Bernstein techniques* Triangulation; Bivariate splines; Interpolation; Scattered data

Indexed keywords

INTERPOLATION; SET THEORY; THEOREM PROVING;

EID: 0040194023     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00387-3     Document Type: Article
Times cited : (8)

References (52)
  • 4
    • 0000522347 scopus 로고
    • The dimension of bivariate spline spaces of smoothness r for degree d≥ 4r+1
    • Alfeld P., Schumaker L.L. The dimension of bivariate spline spaces of smoothness. r for degree d≥ 4r+1 Constr. Approx. 3:1987;189-197.
    • (1987) Constr. Approx. , vol.3 , pp. 189-197
    • Alfeld, P.1    Schumaker, L.L.2
  • 6
    • 0002653115 scopus 로고
    • B-form basics
    • in: G. Farin (Ed.), SIAM, Philadelphia
    • C. de Boor, B-form basics, in: G. Farin (Ed.), Geometric Modeling, SIAM, Philadelphia, 1987, pp. 131-148.
    • (1987) Geometric Modeling , pp. 131-148
    • De Boor, C.1
  • 7
    • 0000141069 scopus 로고
    • Approximation power of smooth bivariate pp functions
    • de Boor C., Höllig K. Approximation power of smooth bivariate pp functions. Math. Z. 197:1988;343-363.
    • (1988) Math. Z. , vol.197 , pp. 343-363
    • De Boor, C.1    Höllig, K.2
  • 8
    • 0011613235 scopus 로고
    • A sharp upper bound on the approximation order of smooth bivariate pp functions
    • de Boor C., Jia Q. A sharp upper bound on the approximation order of smooth bivariate pp functions. J. Approx. Theory. 72:1993;24-33.
    • (1993) J. Approx. Theory , vol.72 , pp. 24-33
    • De Boor, C.1    Jia, Q.2
  • 9
    • 0004053819 scopus 로고
    • CBMS, SIAM, Philadelphia
    • C.K. Chui, Multivariate Splines, CBMS, Vol. 54, SIAM, Philadelphia, 1988.
    • (1988) Multivariate Splines , vol.54
    • Chui, C.K.1
  • 11
    • 0007324146 scopus 로고    scopus 로고
    • Swapping edges of arbitrary triangulations to achieve the optimal order of approximation
    • Chui C.K., Hong D. Swapping edges of arbitrary triangulations to achieve the optimal order of approximation. SIAM J. Numer. Anal. 34:1997;1472-1482.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1472-1482
    • Chui, C.K.1    Hong, D.2
  • 12
    • 0030371938 scopus 로고    scopus 로고
    • 1 quartic spline element for optimal-order approximation
    • 1 quartic spline element for optimal-order approximation Math. Comp. 65:1996;85-98.
    • (1996) Math. Comp. , vol.65 , pp. 85-98
    • Chui, C.K.1    Hong, D.2
  • 13
    • 0001663185 scopus 로고
    • Stability of optimal-order approximation by bivariate splines over arbitrary triangulations
    • Chui C.K., Hong D., Jia Q. Stability of optimal-order approximation by bivariate splines over arbitrary triangulations. Trans. Amer. Math. Soc. 347:1995;3301-3318.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 3301-3318
    • Chui, C.K.1    Hong, D.2    Jia, Q.3
  • 14
    • 0007157878 scopus 로고
    • On bivariate super vertex splines
    • Chui C.K., Lai M.-J. On bivariate super vertex splines. Constr. Approx. 6:1990;399-419.
    • (1990) Constr. Approx. , vol.6 , pp. 399-419
    • Chui, C.K.1    Lai, M.-J.2
  • 16
    • 0007230719 scopus 로고    scopus 로고
    • 1 bivariate splines of degree q ≥ 5
    • M. Daehlen, T. Lyche, & L.L. Schumaker. Nashville: Vanderbilt University Press
    • 1 bivariate splines of degree q ≥ 5 Daehlen M., Lyche T., Schumaker L.L. Mathematical Methods for Curves and Surfaces II. 1998;71-77 Vanderbilt University Press, Nashville.
    • (1998) Mathematical Methods for Curves and Surfaces II , pp. 71-77
    • Davydov, O.1
  • 18
    • 0032047731 scopus 로고    scopus 로고
    • Approximation order of bivariate spline interpolation for arbitrary smoothness
    • Davydov O., Nürnberger G., Zeilfelder F. Approximation order of bivariate spline interpolation for arbitrary smoothness. J. Comput. Appl. Math. 90:1998;117-134.
    • (1998) J. Comput. Appl. Math. , vol.90 , pp. 117-134
    • Davydov, O.1    Nürnberger, G.2    Zeilfelder, F.3
  • 19
    • 0041072293 scopus 로고    scopus 로고
    • Interpolation by cubic splines on triangulations
    • C.K. Chui, & L.L. Schumaker. Nashville: Vanderbilt University Press
    • Davydov O., Nürnberger G., Zeilfelder F. Interpolation by cubic splines on triangulations. Chui C.K., Schumaker L.L. Approximation Theory IX. 1998;17-24 Vanderbilt University Press, Nashville.
    • (1998) Approximation Theory IX , pp. 17-24
    • Davydov, O.1    Nürnberger, G.2    Zeilfelder, F.3
  • 22
    • 46149129389 scopus 로고
    • Triangular Bernstein-Bézier patches
    • Farin G. Triangular Bernstein-Bézier patches. Comput. Aided Geom. Design. 3:1986;83-127.
    • (1986) Comput. Aided Geom. Design , vol.3 , pp. 83-127
    • Farin, G.1
  • 25
    • 0040478102 scopus 로고
    • 1 quartic bivariate splines
    • 1 quartic bivariate splines J. Math. Res. Expo. 11:1991;433-442.
    • (1991) J. Math. Res. Expo. , vol.11 , pp. 433-442
    • Gao, J.1
  • 26
    • 0039885198 scopus 로고
    • 2 finite element and interpolation
    • 2 finite element and interpolation Computing. 50:1993;69-76.
    • (1993) Computing , vol.50 , pp. 69-76
    • Gao, J.1
  • 27
    • 0025468684 scopus 로고
    • Smooth interpolation to scattered data by bivariate piecewise polynomials of odd degree
    • Gmelig Meyling R.H.J., Pfluger P.R. Smooth interpolation to scattered data by bivariate piecewise polynomials of odd degree. Comput. Aided Geom. Design. 7:1990;439-458.
    • (1990) Comput. Aided Geom. Design , vol.7 , pp. 439-458
    • Gmelig Meyling, R.H.J.1    Pfluger, P.R.2
  • 29
    • 0000459863 scopus 로고
    • Super spline spaces of smoothness r and degree d ≥ 3r+2
    • Ibrahim A., Schumaker L.L. Super spline spaces of smoothness. r and degree d ≥ 3r+2 Constr. Approx. 7:1991;401-423.
    • (1991) Constr. Approx. , vol.7 , pp. 401-423
    • Ibrahim, A.1    Schumaker, L.L.2
  • 30
    • 0000161210 scopus 로고
    • 1 cubic splines on a non uniform type-2 triangulation of a rectangular domain
    • 1 cubic splines on a non uniform type-2 triangulation of a rectangular domain C.R. Acad. Sci. Paris Sér. I Math. 314:1992;413-418.
    • (1992) C.R. Acad. Sci. Paris Sér. I Math. , vol.314 , pp. 413-418
    • Jeeawock-Zedek, F.1
  • 31
    • 0039926214 scopus 로고
    • Hermite and Lagrange interpolation by quadratic splines on non-uniform criss-cross triangulations
    • in: P.J. Laurent et al. (Eds.), Wesley, MA
    • F. Jeeawock-Zedek, P. Sablonnière, Hermite and Lagrange interpolation by quadratic splines on non-uniform criss-cross triangulations, in: P.J. Laurent et al. (Eds.), Wavelets, Images and Surface Fitting, Wesley, MA, 1994, pp. 445-452.
    • (1994) Wavelets, Images and Surface Fitting , pp. 445-452
    • Jeeawock-Zedek, F.1    Sablonnière, P.2
  • 35
    • 0009616148 scopus 로고    scopus 로고
    • On the approximation power of bivariate splines
    • Lai M.-J., Schumaker L.L. On the approximation power of bivariate splines. Adv. Comput. Math. 9:1998;251-279.
    • (1998) Adv. Comput. Math. , vol.9 , pp. 251-279
    • Lai, M.-J.1    Schumaker, L.L.2
  • 36
    • 0000675744 scopus 로고    scopus 로고
    • On the approximation power of splines on triangulated quadrangulations
    • Lai M.-J., Schumaker L.L. On the approximation power of splines on triangulated quadrangulations. SIAM J. Numer. Anal. 36:1999;143-159.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 143-159
    • Lai, M.-J.1    Schumaker, L.L.2
  • 37
    • 84966234880 scopus 로고
    • 1 piecewise polynomials of degree n ≥ 5
    • 1 piecewise polynomials of degree n ≥ 5 Math. Comp. 29:1975;736-740.
    • (1975) Math. Comp. , vol.29 , pp. 736-740
    • Morgan, J.1    Scott, R.2
  • 38
    • 0030295901 scopus 로고    scopus 로고
    • Approximation order of bivariate spline interpolation
    • Nürnberger G. Approximation order of bivariate spline interpolation. J. Approx. Theory. 87:1996;117-136.
    • (1996) J. Approx. Theory , vol.87 , pp. 117-136
    • Nürnberger, G.1
  • 40
    • 0001805405 scopus 로고
    • Lagrange and Hermite interpolation by bivariate splines
    • Nürnberger G., Rießinger T. Lagrange and Hermite interpolation by bivariate splines. Numer. Funct. Anal. Optim. 13:1992;75-96.
    • (1992) Numer. Funct. Anal. Optim. , vol.13 , pp. 75-96
    • Nürnberger, G.1    Rießinger, T.2
  • 41
    • 21844490083 scopus 로고
    • Bivariate spline interpolation at grid points
    • Nürnberger G., Rießinger T. Bivariate spline interpolation at grid points. Numer. Math. 71:1995;91-119.
    • (1995) Numer. Math. , vol.71 , pp. 91-119
    • Nürnberger, G.1    Rießinger, T.2
  • 43
    • 4244173431 scopus 로고    scopus 로고
    • Spline interpolation on convex quadrangulations
    • C.K. Chui, & L.L. Schumaker. Nashville: Vanderbilt University Press
    • Nürnberger G., Zeilfelder F. Spline interpolation on convex quadrangulations. Chui C.K., Schumaker L.L. Approximation Theory IX. 1998;259-266 Vanderbilt University Press, Nashville.
    • (1998) Approximation Theory IX , pp. 259-266
    • Nürnberger, G.1    Zeilfelder, F.2
  • 44
    • 84976757268 scopus 로고
    • Piecewise quadratic approximation on triangles
    • Powell M.J.D., Sabin M.A. Piecewise quadratic approximation on triangles. ACM Trans. Math. Software. 4:1977;316-325.
    • (1977) ACM Trans. Math. Software , vol.4 , pp. 316-325
    • Powell, M.J.D.1    Sabin, M.A.2
  • 45
    • 0011554244 scopus 로고
    • Interpolation by bivariate quadratic splines on a four-directional mesh
    • Rießinger T. Interpolation by bivariate quadratic splines on a four-directional mesh. Computing. 49:1992;129-137.
    • (1992) Computing , vol.49 , pp. 129-137
    • Rießinger, T.1
  • 46
    • 0001881630 scopus 로고
    • 2
    • C.K. Chui, L.L. Schumaker, & F.I. Utreras. New York: Academic Press
    • 2 Chui C.K., Schumaker L.L., Utreras F.I. Topics in Multivariate Approximation. 1987;207-217 Academic Press, New York.
    • (1987) Topics in Multivariate Approximation , pp. 207-217
    • Sablonnière, P.1
  • 47
    • 0000998772 scopus 로고
    • Bornes supérieures et inférieures dans l'analyse matricielle des plaques en flexion-torsion
    • Sander G. Bornes supérieures et inférieures dans l'analyse matricielle des plaques en flexion-torsion. Bull. Soc. Roy. Sci. Liège. 33:1964;456-494.
    • (1964) Bull. Soc. Roy. Sci. Liège , vol.33 , pp. 456-494
    • Sander, G.1
  • 48
    • 0024105787 scopus 로고
    • Dual bases for spline spaces on a cell
    • Schumaker L.L. Dual bases for spline spaces on a cell. Comput. Aided Geom. Design. 5:1987;277-284.
    • (1987) Comput. Aided Geom. Design , vol.5 , pp. 277-284
    • Schumaker, L.L.1
  • 49
    • 0001383268 scopus 로고
    • On super splines and finite elements
    • Schumaker L.L. On super splines and finite elements. SIAM J. Numer. Anal. 4:1989;997-1005.
    • (1989) SIAM J. Numer. Anal. , vol.4 , pp. 997-1005
    • Schumaker, L.L.1
  • 52
    • 38249009301 scopus 로고
    • 2 -quintic spline interpolation scheme on triangulation
    • 2 -quintic spline interpolation scheme on triangulation Comp. Aided Geom. Design. 9:1992;379-386.
    • (1992) Comp. Aided Geom. Design , vol.9 , pp. 379-386
    • Wang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.