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Volumn 33, Issue 2, 1996, Pages 571-588

Upper and lower bounds on the dimension of multivariate spline spaces

Author keywords

Bounds on dimensions; Generic dimensions; Multivariate splines; Piecewise polynomial functions; Projection; Triangulations

Indexed keywords


EID: 0039293880     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733030     Document Type: Article
Times cited : (14)

References (16)
  • 1
    • 0009762292 scopus 로고
    • A trivariate Clough-Tocher scheme for tetrahedral data
    • P. ALFELD, A trivariate Clough-Tocher scheme for tetrahedral data, Comput. Aided Geom. Design, 1 (1984), pp. 169-181.
    • (1984) Comput. Aided Geom. Design , vol.1 , pp. 169-181
    • Alfeld, P.1
  • 2
    • 0040478805 scopus 로고
    • A case study of multivariate piecewise polynomials
    • G. Farin, ed., Society for Industrial and Applied Mathematics, Philadelphia, PA
    • _, A case study of multivariate piecewise polynomials, in Geometric Modeling, G. Farin, ed., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1987, pp. 149-160.
    • (1987) Geometric Modeling , pp. 149-160
  • 3
    • 0009127992 scopus 로고
    • On the dimension of multivariate piecewise polynomials
    • D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Harlow, UK
    • _, On the dimension of multivariate piecewise polynomials, in Numerical Analysis, D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Harlow, UK, 1986, pp. 1-23.
    • (1986) Numerical Analysis , pp. 1-23
  • 4
    • 0001781796 scopus 로고
    • Scattered data interpolation in three or more variables
    • T. Lyche and L.L. Schumaker, eds., Academic Press, New York
    • _, Scattered data interpolation in three or more variables, in Mathematical Methods in Computer Aided Geometric Design, T. Lyche and L.L. Schumaker, eds., Academic Press, New York, 1989, pp. 1-33.
    • (1989) Mathematical Methods in Computer Aided Geometric Design , pp. 1-33
  • 5
    • 0026282888 scopus 로고
    • Algorithm 701, Goliath, a software system for the exact analysis of rectangular rank-deficient sparse rational linear systems
    • P. ALFELD AND D. EYRE, Algorithm 701, Goliath, A software system for the exact analysis of rectangular rank-deficient sparse rational linear systems, ACM Trans. Math. Software, 17 (1991), pp. 519-532.
    • (1991) ACM Trans. Math. Software , vol.17 , pp. 519-532
    • Alfeld, P.1    Eyre, D.2
  • 6
    • 0026301007 scopus 로고
    • The exact analysis of sparse rectangular linear systems
    • _, The exact analysis of sparse rectangular linear systems, ACM Trans. Math. Software, 17 (1991), pp. 502-518.
    • (1991) ACM Trans. Math. Software , vol.17 , pp. 502-518
  • 7
    • 38249009107 scopus 로고
    • On dimension and existence of local bases for multivariate spline spaces
    • P. ALFELD, L. L. SCHUMAKER, AND M. SIRVENT, On dimension and existence of local bases for multivariate spline spaces, J. Approx. Theory, 70 (1992), pp. 243-264.
    • (1992) J. Approx. Theory , vol.70 , pp. 243-264
    • Alfeld, P.1    Schumaker, L.L.2    Sirvent, M.3
  • 9
    • 51249172414 scopus 로고
    • A dimension series for multivariate splines
    • L. H. BILLERA AND L. L. ROSE, A dimension series for multivariate splines, Discrete & Comput. Geom., 6 (1991), pp. 107-128.
    • (1991) Discrete & Comput. Geom. , vol.6 , pp. 107-128
    • Billera, L.H.1    Rose, L.L.2
  • 10
    • 0003193239 scopus 로고
    • Some aspects of the topology of 3-manifolds related to the Poincaré conjecture
    • T.L. Saaty, ed., Wiley, New York
    • R. H. BING, Some aspects of the topology of 3-manifolds related to the Poincaré conjecture, in Lectures on Modern Mathematics, Vol. 2, T.L. Saaty, ed., Wiley, New York, 1964, pp. 93-128.
    • (1964) Lectures on Modern Mathematics , vol.2 , pp. 93-128
    • Bing, R.H.1
  • 11
    • 0010394606 scopus 로고
    • Multivariate piecewise polynomials
    • A. Iserless, ed., Cambridge University Press, London
    • C. DE BOOR, Multivariate piecewise polynomials, in Acta Numerica, A. Iserless, ed., Cambridge University Press, London, 1993, pp. 65-109.
    • (1993) Acta Numerica , pp. 65-109
    • De Boor, C.1
  • 13
    • 0023015266 scopus 로고
    • Properties of n-dimensional triangulations
    • C. L. LAWSON, Properties of n-dimensional triangulations, Comput. Aided Geom. Design, 3 (1986), pp. 231-247.
    • (1986) Comput. Aided Geom. Design , vol.3 , pp. 231-247
    • Lawson, C.L.1
  • 14
    • 84966234880 scopus 로고
    • 1 piecewise polynomials in two variables
    • 1 piecewise polynomials in two variables, Math. Comp., 29 (1975), pp. 736-740.
    • (1975) Math. Comp. , vol.29 , pp. 736-740
    • Morgan, J.1    Scott, R.2
  • 15
    • 0039855549 scopus 로고
    • An unshellable triangulation of a tetrahedron
    • M. E. RUDIN, An unshellable triangulation of a tetrahedron, Bull. Amer. Math. Soc., 64 (1958), pp. 90-91.
    • (1958) Bull. Amer. Math. Soc. , vol.64 , pp. 90-91
    • Rudin, M.E.1
  • 16
    • 85033762996 scopus 로고
    • Private communication, York University
    • W. WHITELEY, Private communication, York University, 1993.
    • (1993)
    • Whiteley, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.