메뉴 건너뛰기




Volumn 22, Issue 1, 1999, Pages 41-52

Error analysis of corner cutting algorithms

Author keywords

Backward error; Condition number; Corner cutting; De Boor Cox algorithm; De Casteljau algorithm; Forward error; Roundoff error; Running error

Indexed keywords


EID: 0042579543     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019190220312     Document Type: Article
Times cited : (29)

References (20)
  • 1
    • 0031162523 scopus 로고    scopus 로고
    • Corner cutting curves and a new characterization of Bézier and B-spline curves
    • G. Aumann, Corner cutting curves and a new characterization of Bézier and B-spline curves, Computer-Aided Geom. Design 14 (1997) 449-474.
    • (1997) Computer-Aided Geom. Design , vol.14 , pp. 449-474
    • Aumann, G.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
    • 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
    • 0030516403 scopus 로고    scopus 로고
    • On the optimal stability of Bernstein basis
    • R.T. Farouki and T.N.T. Goodman, On the optimal stability of Bernstein basis, Math. Comp. 65 (1996) 1553-1566.
    • (1996) Math. Comp. , vol.65 , pp. 1553-1566
    • Farouki, R.T.1    Goodman, T.N.T.2
  • 6
    • 0023455805 scopus 로고
    • On the numerical condition of polynomials in Bernstein form
    • R.T. Farouki and V.T. Rajan, On the numerical condition of polynomials in Bernstein form, Computer-Aided Geom. Design 4 (1987) 191-216.
    • (1987) Computer-Aided Geom. Design , vol.4 , pp. 191-216
    • Farouki, R.T.1    Rajan, V.T.2
  • 7
    • 0005467468 scopus 로고
    • Corner cutting algorithms and totally positive matrices
    • eds. P.J. Laurent, A. Le Méhauté and L.L. Schumaker A.K. Peters, Wellesley
    • M. Gasca and J.M. Peña, Corner cutting algorithms and totally positive matrices, in: Curves and Surfaces in Geometric Design, eds. P.J. Laurent, A. Le Méhauté and L.L. Schumaker (A.K. Peters, Wellesley, 1994) pp. 177-184.
    • (1994) Curves and Surfaces in Geometric Design , pp. 177-184
    • Gasca, M.1    Peña, J.M.2
  • 8
    • 0006408133 scopus 로고    scopus 로고
    • On factorizations of totally positive matrices
    • eds. M. Gasca and C.A. Micchelli Kluwer Academic, Dordrecht
    • M. Gasca and J.M. Peña, On factorizations of totally positive matrices, in: Total Positivity and its Applications, eds. M. Gasca and C.A. Micchelli (Kluwer Academic, Dordrecht, 1996) pp. 109-130.
    • (1996) Total Positivity and Its Applications , pp. 109-130
    • Gasca, M.1    Peña, J.M.2
  • 9
    • 0001020447 scopus 로고
    • Shape preserving representations
    • eds. T. Lyche and L.L. Schumaker Academic Press, Boston
    • T.N.T. Goodman, Shape preserving representations, in: Mathematical Methods in CAGD, eds. T. Lyche and L.L. Schumaker (Academic Press, Boston, 1989) pp. 333-357.
    • (1989) Mathematical Methods in CAGD , pp. 333-357
    • Goodman, T.N.T.1
  • 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, Computer-Aided Geom. Design 8 (1991) 115-121.
    • (1991) Computer-Aided Geom. Design , vol.8 , pp. 115-121
    • Goodman, T.N.T.1    Said, H.B.2
  • 13
    • 0042301405 scopus 로고
    • Error bounds for polynomial evaluation and complex arithmetic
    • F.W.J. Olver, Error bounds for polynomial evaluation and complex arithmetic, IMA J. Numer. Anal. 2 (1982) 377-406.
    • (1982) IMA J. Numer. Anal. , vol.2 , pp. 377-406
    • Olver, F.W.J.1
  • 14
    • 0030737321 scopus 로고    scopus 로고
    • Shape preserving representations for trigonometric polynomial curves
    • J.M. Peña, Shape preserving representations for trigonometric polynomial curves, Computer-Aided Geom. Desing 14 (1997) 5-11.
    • (1997) Computer-Aided Geom. Desing , vol.14 , pp. 5-11
    • Peña, J.M.1
  • 15
    • 0040453764 scopus 로고    scopus 로고
    • B-splines and optimal stability
    • J.M. Peña, B-splines and optimal stability, Math. Comp. 66 (1997) 1555-1560.
    • (1997) Math. Comp. , vol.66 , pp. 1555-1560
    • Peña, J.M.1
  • 16
    • 84968490755 scopus 로고
    • Error analysis of the algorithm for shifting the zeros of a polynomial by synthetic division
    • G.W. Stewart, Error analysis of the algorithm for shifting the zeros of a polynomial by synthetic division, Math. Comp. 25 (1971) 135-139.
    • (1971) Math. Comp. , vol.25 , pp. 135-139
    • Stewart, G.W.1
  • 17
    • 0041800336 scopus 로고
    • Error analysis of splitting algorithms for polynomials
    • N.K. Tsao, Error analysis of splitting algorithms for polynomials, Numer. Math. 32 (1979) 409-421.
    • (1979) Numer. Math. , vol.32 , pp. 409-421
    • Tsao, N.K.1
  • 18
    • 34250956078 scopus 로고
    • The evaluation of the zeros of ill-conditioned polynomials, Parts I and II
    • J.H. Wilkinson, The evaluation of the zeros of ill-conditioned polynomials, Parts I and II, Numer. Math. 1 (1959) 150-166 and 167-180.
    • (1959) Numer. Math. , vol.1 , pp. 150-166
    • Wilkinson, J.H.1
  • 19
    • 0003227519 scopus 로고
    • Rounding Errors in Algebraic Processes
    • Her Majesty's Stationery Office, London
    • J.H. Wilkinson, Rounding Errors in Algebraic Processes, Notes on Applied Science, Vol. 32 (Her Majesty's Stationery Office, London, 1963).
    • (1963) Notes on Applied Science , vol.32
    • Wilkinson, J.H.1
  • 20
    • 0016105172 scopus 로고
    • Rounding error analysis for the evaluation of a polynomial and some of its derivatives
    • H. Wozniakowski, Rounding error analysis for the evaluation of a polynomial and some of its derivatives, SIAM J. Numer. Anal. 11 (1974) 780-787.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 780-787
    • Wozniakowski, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.