메뉴 건너뛰기




Volumn 12, Issue 8, 2005, Pages 685-698

Structured matrix methods for CAGD: An application to computing the resultant of polynomials in the Bernstein basis

Author keywords

B zier curves; Bernstein polynomials; Bezoutian matrices; Computer aided geometric design; Fraction free Gaussian elimination; Numerical computations

Indexed keywords


EID: 26644461682     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.444     Document Type: Conference Paper
Times cited : (9)

References (25)
  • 1
    • 0345381918 scopus 로고    scopus 로고
    • An application of fast factorization algorithms in computer aided geometric design
    • Casciola G, Fabbri F, Montefusco LB. An application of fast factorization algorithms in computer aided geometric design. Linear Algebra and Its Applications 2003; 366:121-138.
    • (2003) Linear Algebra and its Applications , vol.366 , pp. 121-138
    • Casciola, G.1    Fabbri, F.2    Montefusco, L.B.3
  • 3
    • 0006590578 scopus 로고    scopus 로고
    • Current trends in geometric modeling and selected computational applications
    • Farin GE, Hamann B. Current trends in geometric modeling and selected computational applications. Journal of Computational Physics 1997; 138(1):1-15.
    • (1997) Journal of Computational Physics , vol.138 , Issue.1 , pp. 1-15
    • Farin, G.E.1    Hamann, B.2
  • 5
    • 33747958715 scopus 로고
    • Fundamental techniques for geometric and solid modeling
    • Academic Press: San Diego, CA
    • Hoffmann CM, Vaněček Jr G. Fundamental techniques for geometric and solid modeling. Control and Dynamic Systems. Academic Press: San Diego, CA, 1991; 48:101-165.
    • (1991) Control and Dynamic Systems , vol.48 , pp. 101-165
    • Hoffmann, C.M.1    Vaněček Jr., G.2
  • 6
    • 0003519398 scopus 로고
    • A K Peters Ltd.: Wellesley, MA, (Translated from the 1992 German edition by Larry L. Schumaker)
    • Hoschek J, Lasser D. Fundamentals of Computer Aided Geometric Design. A K Peters Ltd.: Wellesley, MA, 1993 (Translated from the 1992 German edition by Larry L. Schumaker).
    • (1993) Fundamentals of Computer Aided Geometric Design
    • Hoschek, J.1    Lasser, D.2
  • 7
    • 0010953053 scopus 로고
    • Algebraic geometry for surface and solid modeling
    • SIAM: Philadelphia, PA
    • Sederberg TW. Algebraic geometry for surface and solid modeling. Geometric Modeling. SIAM: Philadelphia, PA, 1987; 29-42.
    • (1987) Geometric Modeling , pp. 29-42
    • Sederberg, T.W.1
  • 8
    • 4544263996 scopus 로고    scopus 로고
    • Algebraic methods for computer aided geometric design
    • North-Holland: Amsterdam
    • Sederberg TW, Zheng J. Algebraic methods for computer aided geometric design. Handbook of Computer Aided Geometric Design. North-Holland: Amsterdam, 2002; 363-387.
    • (2002) Handbook of Computer Aided Geometric Design , pp. 363-387
    • Sederberg, T.W.1    Zheng, J.2
  • 10
    • 0026102939 scopus 로고
    • On the stability of transformations between power and Bernstein polynomials
    • Farouki RT. On the stability of transformations between power and Bernstein polynomials. Computer Aided Geometric Design 1991; 8:29-36.
    • (1991) Computer Aided Geometric Design , vol.8 , pp. 29-36
    • Farouki, R.T.1
  • 11
    • 0023455805 scopus 로고
    • On the numerical condition of polynomials in Bernstein form
    • Farouki RT, Rajan VT. On the numerical condition of polynomials in Bernstein form. Computer Aided Geometric Design 1987; 4:191-216.
    • (1987) Computer Aided Geometric Design , vol.4 , pp. 191-216
    • Farouki, R.T.1    Rajan, V.T.2
  • 12
    • 0346724613 scopus 로고    scopus 로고
    • The transformation of the companion matrix resultant between the power and the Bernstein polynomial bases
    • Winkler JR. The transformation of the companion matrix resultant between the power and the Bernstein polynomial bases. Applied Numerical Mathematics 2004; 48:113-126.
    • (2004) Applied Numerical Mathematics , vol.48 , pp. 113-126
    • Winkler, J.R.1
  • 13
    • 0347610077 scopus 로고    scopus 로고
    • The Sylvester resultant matrix for Bernstein polynomials
    • Saint-Malo Lyche T, Mazure ML, Schumaker LL (eds). Nashboro Press: Brentwood, Tennessee, U.S.A.
    • Winkler JR, Goldman RN. The Sylvester resultant matrix for Bernstein polynomials. In Curve and Surface Design, Saint-Malo 2002, Lyche T, Mazure ML, Schumaker LL (eds). Nashboro Press: Brentwood, Tennessee, U.S.A., 2003; 407-416.
    • (2002) Curve and Surface Design , pp. 407-416
    • Winkler, J.R.1    Goldman, R.N.2
  • 14
    • 26644437843 scopus 로고    scopus 로고
    • Properties of the companion matrix resultant for Bernstein polynomials
    • Winkler JR, Niranjan M (eds). Kluwer Academic Publishers: Massachusetts, U.S.A.
    • Winkler JR. Properties of the companion matrix resultant for Bernstein polynomials. In Uncertainty in Geometric Computations, Winkler JR, Niranjan M (eds). Kluwer Academic Publishers: Massachusetts, U.S.A., 2002; 185-198.
    • (2002) Uncertainty in Geometric Computations , pp. 185-198
    • Winkler, J.R.1
  • 15
    • 84867960648 scopus 로고    scopus 로고
    • A companion matrix resultant for Bernstein polynomials
    • Winkler JR. A companion matrix resultant for Bernstein polynomials. Linear Algebra and Its Applications 2003; 362:153-175.
    • (2003) Linear Algebra and Its Applications , vol.362 , pp. 153-175
    • Winkler, J.R.1
  • 16
    • 84968497774 scopus 로고
    • Sylvester's identity and multistep integer-preserving Gaussian elimination
    • Bareiss EH. Sylvester's identity and multistep integer-preserving Gaussian elimination. Mathematics of Computation 1968; 22:565-578.
    • (1968) Mathematics of Computation , vol.22 , pp. 565-578
    • Bareiss, E.H.1
  • 17
    • 0041577194 scopus 로고    scopus 로고
    • Fast fraction-free triangularization of Bezoutians with applications to sub-resultant chain computation
    • Bini DA, Gemignani L. Fast fraction-free triangularization of Bezoutians with applications to sub-resultant chain computation. Linear Algebra and Its Applications 1998; 284:19-39.
    • (1998) Linear Algebra and Its Applications , vol.284 , pp. 19-39
    • Bini, D.A.1    Gemignani, L.2
  • 19
    • 0038375748 scopus 로고    scopus 로고
    • Algorithm 812: BPOLY: an object-oriented library of numerical algorithms for polynomials in Bernstein form
    • Tsai YF, Farouki RT. Algorithm 812: BPOLY: an object-oriented library of numerical algorithms for polynomials in Bernstein form. ACM Transactions on Mathematical Software (TOMS) 2001; 27:267-296.
    • (2001) ACM Transactions on Mathematical Software (TOMS) , vol.27 , pp. 267-296
    • Tsai, Y.F.1    Farouki, R.T.2
  • 20
    • 26644458514 scopus 로고
    • Forms of the resultant of two polynomials
    • Barnett S. Forms of the resultant of two polynomials. American Mathematical Monthly 1986; 93(7):551-552.
    • (1986) American Mathematical Monthly , vol.93 , Issue.7 , pp. 551-552
    • Barnett, S.1
  • 21
    • 0029247028 scopus 로고
    • Fast parallel computation of the polynomial remainder sequence via Bézout and Hankel matrices
    • Bini D, Gemignani L. Fast parallel computation of the polynomial remainder sequence via Bézout and Hankel matrices. SIAM Journal on Computing 1995; 24(1):63-77.
    • (1995) SIAM Journal on Computing , vol.24 , Issue.1 , pp. 63-77
    • Bini, D.1    Gemignani, L.2
  • 23
    • 0000665794 scopus 로고
    • Displacement structure: Theory and applications
    • Kailath T, Sayed AH. Displacement structure: theory and applications. SIAM Review 1995; 37(3):297-386.
    • (1995) SIAM Review , vol.37 , Issue.3 , pp. 297-386
    • Kailath, T.1    Sayed, A.H.2
  • 25
    • 0043226037 scopus 로고    scopus 로고
    • Application of Bernstein expansion to the solution of control problems. Applications to control, signals and systems
    • Garloff J. Application of Bernstein expansion to the solution of control problems. Applications to control, signals and systems. Reliable Computing 2000; 6(3):303-320.
    • (2000) Reliable Computing , vol.6 , Issue.3 , pp. 303-320
    • Garloff, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.