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Volumn 5081 LNAI, Issue , 2008, Pages 72-86

Basis-independent polynomial division algorithm applied to division in lagrange and bernstein basis

Author keywords

Bernstein basis; Lagrange basis; Polynomial division

Indexed keywords

ALGORITHMS; AMBER; LAGRANGE MULTIPLIERS; MATHEMATICAL TECHNIQUES; POLYNOMIALS; TREES (MATHEMATICS);

EID: 55249092482     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-87827-8_6     Document Type: Conference Paper
Times cited : (3)

References (24)
  • 1
    • 55249090643 scopus 로고    scopus 로고
    • Amiraslani, A.: Dividing polynomials when you only know their values. In: Gonzalez-Vega, L., Recio, T. (eds.) Proceedings of Encuentros de Álgebra Computacional y Aplicaciones (EACA) 2004, pp. 5-10 (2004), http://www.orcca.on. ca/TechReports/2004/TR-04-01.html
    • Amiraslani, A.: Dividing polynomials when you only know their values. In: Gonzalez-Vega, L., Recio, T. (eds.) Proceedings of Encuentros de Álgebra Computacional y Aplicaciones (EACA) 2004, pp. 5-10 (2004), http://www.orcca.on. ca/TechReports/2004/TR-04-01.html
  • 5
    • 0043181027 scopus 로고
    • Division of generalized polynomials using the comrade matrix
    • Barnett, S.: Division of generalized polynomials using the comrade matrix. Linear Algebra Appl. 60, 159-175 (1984)
    • (1984) Linear Algebra Appl , vol.60 , pp. 159-175
    • Barnett, S.1
  • 6
    • 38249031267 scopus 로고
    • Euclidean remainders for generalized polynomials
    • Barnett, S.: Euclidean remainders for generalized polynomials. Linear Algebra Appl. 99. 111-122 (1988)
    • (1988) Linear Algebra Appl , vol.99 , pp. 111-122
    • Barnett, S.1
  • 8
    • 26644461682 scopus 로고    scopus 로고
    • Structured matrix methods for CAGD: An application to computing the resultant of polynomials in the Bernstein basis
    • Bini, D.A., Gemignani, L., Winkler, J.R.: Structured matrix methods for CAGD: an application to computing the resultant of polynomials in the Bernstein basis. Numer. Linear Algebra Appl. 12(8), 685-698 (2005)
    • (2005) Numer. Linear Algebra Appl , vol.12 , Issue.8 , pp. 685-698
    • Bini, D.A.1    Gemignani, L.2    Winkler, J.R.3
  • 9
    • 21844434668 scopus 로고    scopus 로고
    • Polynomial evaluation and interpolation on special sets of points
    • Bostan, A., Sehest, É.: Polynomial evaluation and interpolation on special sets of points. J. Complexity 21(4), 420-446 (2005)
    • (2005) J. Complexity , vol.21 , Issue.4 , pp. 420-446
    • Bostan, A.1    Sehest, E.2
  • 10
    • 33748955519 scopus 로고    scopus 로고
    • Cheng, H., Labahn, G.: On computing polynomial GCDs in alternate bases. In: ISSAC 2006, pp. 47-54. ACM. New York (2006)
    • Cheng, H., Labahn, G.: On computing polynomial GCDs in alternate bases. In: ISSAC 2006, pp. 47-54. ACM. New York (2006)
  • 11
    • 34547226168 scopus 로고    scopus 로고
    • Generalized companion matrices in the lagrange basis
    • Gonzalez-Vega, L, Recio. T, eds
    • Corless, R.: Generalized companion matrices in the lagrange basis. In: Gonzalez-Vega, L., Recio. T. (eds.) Proceedings of Encuentros de Álgebra Computacional y Aplicaciones (EACA 2004), pp. 317-322 (2004), http://www.apmaths.uwo.ca/~rcorless/frames/PAPERS/PABV/EACA2004Corless.pdf
    • (2004) Proceedings of Encuentros de Álgebra Computacional y Aplicaciones (EACA , pp. 317-322
    • Corless, R.1
  • 12
    • 0036657905 scopus 로고    scopus 로고
    • Barnett's theorems about the greatest common divisor of several univariate polynomials through Bezout-like matrices
    • Diaz-Toca, G.M., Gonzalez-Vega, L.: Barnett's theorems about the greatest common divisor of several univariate polynomials through Bezout-like matrices. J. Symbolic Comput. 34(1), 59-81 (2002)
    • (2002) J. Symbolic Comput , vol.34 , Issue.1 , pp. 59-81
    • Diaz-Toca, G.M.1    Gonzalez-Vega, L.2
  • 13
    • 0030516403 scopus 로고    scopus 로고
    • On the optimal stability of the Bernstein basis
    • Farouki, R.T., Goodman, T.N.T.: On the optimal stability of the Bernstein basis. Math. Comp. 65(216), 1553-1566 (1996)
    • (1996) Math. Comp , vol.65 , Issue.216 , pp. 1553-1566
    • Farouki, R.T.1    Goodman, T.N.T.2
  • 14
    • 55249112711 scopus 로고    scopus 로고
    • Gemignani, L.: Manipulating polynomials in generalized form. Technical Report TR-96-14, Università di Pisa, Departmento di Informatica, Corso Italia 40, 56125 Pisa, Italy (December 1996)
    • Gemignani, L.: Manipulating polynomials in generalized form. Technical Report TR-96-14, Università di Pisa, Departmento di Informatica, Corso Italia 40, 56125 Pisa, Italy (December 1996)
  • 15
    • 1542301130 scopus 로고    scopus 로고
    • Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling
    • 1st edn, Morgan Kaufmann, San Francisco
    • Goldman, R.: Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling, 1st edn. The Morgan Kaufmann Series in Computer Graphics. Morgan Kaufmann, San Francisco (2002)
    • (2002) The Morgan Kaufmann Series in Computer Graphics
    • Goldman, R.1
  • 16
    • 0031543115 scopus 로고    scopus 로고
    • Generalized polynomial bases and the Bezoutian
    • Mani, V., Hartwig, R.E.: Generalized polynomial bases and the Bezoutian. Linear Algebra Appl. 251, 293-320 (1997)
    • (1997) Linear Algebra Appl , vol.251 , pp. 293-320
    • Mani, V.1    Hartwig, R.E.2
  • 17
    • 49349126348 scopus 로고
    • Greatest common divisor of generalized polynomial and polynomial matrices
    • Maroulas, J., Barnett, S.: Greatest common divisor of generalized polynomial and polynomial matrices. Linear Algebra Appl. 22, 195-210 (1978)
    • (1978) Linear Algebra Appl , vol.22 , pp. 195-210
    • Maroulas, J.1    Barnett, S.2
  • 18
    • 12944292003 scopus 로고    scopus 로고
    • Society for Industrial and Applied Mathematics. SIAM, Philadelphia
    • Stetter, H.J.: Numerical polynomial algebra. Society for Industrial and Applied Mathematics. SIAM, Philadelphia (2004)
    • (2004) Numerical polynomial algebra
    • Stetter, H.J.1
  • 19
    • 0038375748 scopus 로고    scopus 로고
    • Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form
    • Tsai, Y.-F., Farouki, R.T.: Algorithm 812: BPOLY: An object-oriented library of numerical algorithms for polynomials in Bernstein form. ACM Transactions on Mathematical Software 27(2), 267-296 (2001)
    • (2001) ACM Transactions on Mathematical Software , vol.27 , Issue.2 , pp. 267-296
    • Tsai, Y.-F.1    Farouki, R.T.2
  • 22
    • 0034362277 scopus 로고    scopus 로고
    • A resultant matrix for scaled Bernstein polynomials
    • Winkler, J.R.: A resultant matrix for scaled Bernstein polynomials. Linear Algebra Appl. 319(1-3), 179-191 (2000)
    • (2000) Linear Algebra Appl , vol.319 , Issue.1-3 , pp. 179-191
    • Winkler, J.R.1
  • 23
    • 55249085824 scopus 로고    scopus 로고
    • Winkler, J.R.: Properties of the companion matrix resultant for Bernstein polynomials. In: Uncertainty in geometric computations. Kluwer Internat. Ser. Engrg. Comput. Sci., 704, pp. 185-198. Kluwer Acad. Publ., Boston (2002)
    • Winkler, J.R.: Properties of the companion matrix resultant for Bernstein polynomials. In: Uncertainty in geometric computations. Kluwer Internat. Ser. Engrg. Comput. Sci., vol. 704, pp. 185-198. Kluwer Acad. Publ., Boston (2002)
  • 24
    • 84867960648 scopus 로고    scopus 로고
    • A companion matrix resultant for Bernstein polynomials
    • Winkler, J.R.: A companion matrix resultant for Bernstein polynomials. Linear Algebra Appl. 362, 153-175 (2003)
    • (2003) Linear Algebra Appl , vol.362 , pp. 153-175
    • Winkler, J.R.1


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