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Volumn 20, Issue 1-3, 2004, Pages 177-203

Blossoms and optimal bases

Author keywords

B spline basis; Bernstein basis; Blossoming; Chebyshev blossoming; Corner cutting algorithms; Extended Chebyshev spaces; Total positivity

Indexed keywords


EID: 0346494933     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025855123163     Document Type: Conference Paper
Times cited : (66)

References (26)
  • 1
    • 0030493646 scopus 로고    scopus 로고
    • De Boor-Fix dual functionals and algorithms for Tchebychevian B-splines curves
    • P.J. Barry, De Boor-Fix dual functionals and algorithms for Tchebychevian B-splines curves, Constr. Approx. 12 (1996) 385-408.
    • (1996) Constr. Approx. , vol.12 , pp. 385-408
    • Barry, P.J.1
  • 2
    • 0000396870 scopus 로고
    • Shape preserving representations and optimality of the Bernstein basis
    • J.-M. Carnicer and J.-M. Peña, Shape preserving representations and optimality of the Bernstein basis, Adv. Comput. Math. 1 (1993) 173-196.
    • (1993) Adv. Comput. Math. , vol.1 , pp. 173-196
    • Carnicer, J.-M.1    Peña, J.-M.2
  • 3
    • 0028736414 scopus 로고
    • Totally positive bases for shape preserving curve design and optimality of B-splines
    • J.-M. Carnicer and J.-M. Peña, Totally positive bases for shape preserving curve design and optimality of B-splines, Comput. Aided Geom. Design 11 (1994) 633-654.
    • (1994) Comput. Aided Geom. Design , vol.11 , pp. 633-654
    • Carnicer, J.-M.1    Peña, J.-M.2
  • 4
    • 0001967871 scopus 로고    scopus 로고
    • Total positivity and optimal bases
    • eds. M. Gasca and C.A. Micchelli (Kluwer Academic, Dordrecht)
    • J.-M. Carnicer and J.-M. Peña, Total positivity and optimal bases, in: Total Positivity and its Applications, eds. M. Gasca and C.A. Micchelli (Kluwer Academic, Dordrecht, 1996) pp. 133-155.
    • (1996) Total Positivity and Its Applications , pp. 133-155
    • Carnicer, J.-M.1    Peña, J.-M.2
  • 5
    • 84966241136 scopus 로고
    • On monotone and convex spline interpolation
    • P. Costantini, On monotone and convex spline interpolation, Math. Comp. 46 (1986) 203-214.
    • (1986) Math. Comp. , vol.46 , pp. 203-214
    • Costantini, P.1
  • 6
    • 0034188372 scopus 로고    scopus 로고
    • Curve and surface construction using variable degree polynomial splines
    • P. Costantini, Curve and surface construction using variable degree polynomial splines, Comput. Aided Geom. Design 17 (2000) 419-446.
    • (2000) Comput. Aided Geom. Design , vol.17 , pp. 419-446
    • Costantini, P.1
  • 7
    • 0001020447 scopus 로고
    • Shape preserving representations
    • eds. T. Lyche and L.L. Schumaker (Academic Press, New York)
    • T.N.T. Goodman, Shape preserving representations, in: Mathematical Methods in Computer Aided Geometric Design, eds. T. Lyche and L.L. Schumaker (Academic Press, New York, 1989) pp. 333-357.
    • (1989) Mathematical Methods in Computer Aided Geometric Design , pp. 333-357
    • Goodman, T.N.T.1
  • 8
    • 0001156074 scopus 로고    scopus 로고
    • Total positivity and the shape of curves
    • eds. M. Gasca and C.A. Micchelli (Kluwer Academic, Dordrecht)
    • T.N.T. Goodman, Total positivity and the shape of curves, in: Total Positivity and its Applications, eds. M. Gasca and C.A. Micchelli (Kluwer Academic, Dordrecht, 1996) pp. 157-186.
    • (1996) Total Positivity and Its Applications , pp. 157-186
    • Goodman, T.N.T.1
  • 9
    • 0042239287 scopus 로고    scopus 로고
    • Blossoming beyond extended Chebyshev spaces
    • T.N.T. Goodman and M.-L. Mazure, Blossoming beyond extended Chebyshev spaces, J. Approx. Theory 109 (2001) 48-81.
    • (2001) J. Approx. Theory , vol.109 , pp. 48-81
    • Goodman, T.N.T.1    Mazure, M.-L.2
  • 10
    • 38249031099 scopus 로고
    • Corner cutting algorithms for the Bézier representation of free form curves
    • T.N.T. Goodman and C.A. Micchelli, Corner cutting algorithms for the Bézier representation of free form curves, Linear Algebra Appl. 99 (1988) 225-252.
    • (1988) Linear Algebra Appl. , vol.99 , pp. 225-252
    • Goodman, T.N.T.1    Micchelli, C.A.2
  • 11
    • 0026156565 scopus 로고
    • Shape preserving properties of the generalized Ball basis
    • T.N.T. Goodman and H.B. Said, Shape preserving properties of the generalized Ball basis, Comput. Aided Geom. Design 8 (1991) 115-121.
    • (1991) Comput. Aided Geom. Design , vol.8 , pp. 115-121
    • Goodman, T.N.T.1    Said, H.B.2
  • 12
    • 0000421970 scopus 로고
    • Convexity preserving polynomial splines of non-uniform degree
    • P.D. Kaklis and D.G. Pandelis, Convexity preserving polynomial splines of non-uniform degree, IMA J. Numer. Anal. 10 (1990) 223-234.
    • (1990) IMA J. Numer. Anal. , vol.10 , pp. 223-234
    • Kaklis, P.D.1    Pandelis, D.G.2
  • 13
    • 0004167764 scopus 로고
    • Stanford Univ. Press, Stanford
    • S. Karlin, Total Positivity (Stanford Univ. Press, Stanford, 1968).
    • (1968) Total Positivity
    • Karlin, S.1
  • 16
    • 0033249423 scopus 로고    scopus 로고
    • Blossoming: A geometrical approach
    • M.-L. Mazure, Blossoming: a geometrical approach, Constr. Approx. 15 (1999) 33-68.
    • (1999) Constr. Approx. , vol.15 , pp. 33-68
    • Mazure, M.-L.1
  • 18
    • 0042579540 scopus 로고    scopus 로고
    • Bernstein bases in Müntz spaces
    • M.-L. Mazure, Bernstein bases in Müntz spaces, Numer. Algorithms 22 (1999) 285-304.
    • (1999) Numer. Algorithms , vol.22 , pp. 285-304
    • Mazure, M.-L.1
  • 19
    • 0035625535 scopus 로고    scopus 로고
    • Chebyshev splines beyond total positivity
    • M.-L. Mazure, Chebyshev splines beyond total positivity, Adv. Comput. Math. 14 (2001) 129-156.
    • (2001) Adv. Comput. Math , vol.14 , pp. 129-156
    • Mazure, M.-L.1
  • 20
    • 0035304141 scopus 로고    scopus 로고
    • Quasi-Chebyshev splines with connection matrices. Application to variable degree polynomial splines
    • M.-L. Mazure, Quasi-Chebyshev splines with connection matrices. Application to variable degree polynomial splines, Comput. Aided Geom. Design 18 (2001) 287-298.
    • (2001) Comput. Aided Geom. Design , vol.18 , pp. 287-298
    • Mazure, M.-L.1
  • 21
    • 0348060034 scopus 로고    scopus 로고
    • B-spline bases and osculating flats: One result of H.-P. Seidel revisited
    • to appear
    • M.-L. Mazure, B-spline bases and osculating flats: One result of H.-P. Seidel revisited, to appear in Math. Modelling Numer. Anal.
    • Math. Modelling Numer. Anal.
    • Mazure, M.-L.1
  • 23
    • 0001159305 scopus 로고    scopus 로고
    • Tchebycheff Curves
    • eds. M. Gasca and C.A. Micchelli (Kluwer Academic, Dordrecht)
    • M.-L. Mazure and H. Pottmann, Tchebycheff Curves, in: Total Positivity and its Applications, eds. M. Gasca and C.A. Micchelli (Kluwer Academic, Dordrecht, 1996) pp. 187-218.
    • (1996) Total Positivity and Its Applications , pp. 187-218
    • Mazure, M.-L.1    Pottmann, H.2
  • 24
    • 0027640834 scopus 로고
    • The geometry of Tchebycheffian splines
    • H. Pottmann, The geometry of Tchebycheffian splines, Comput. Aided Geom. Design 10 (1993) 181-210.
    • (1993) Comput. Aided Geom. Design , vol.10 , pp. 181-210
    • Pottmann, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.