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Volumn 60, Issue 1-2, 2010, Pages 94-114

The ERES method for computing the approximate GCD of several polynomials

Author keywords

Approximate greatest common divisor; Gaussian elimination; Partial SVD; Symbolic numeric computations

Indexed keywords

APPROXIMATE GCD; APPROXIMATE SOLUTION; BASIC PRINCIPLES; COMPUTATIONAL PROPERTIES; EFFICIENT IMPLEMENTATION; GAUSSIAN ELIMINATION; GREATEST COMMON DIVISORS; HYBRID IMPLEMENTATION; NUMERIC COMPUTATION; OPTIMIZATION ALGORITHMS; PROJECTIVE SPACES; WORK FOCUS;

EID: 71549165486     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2009.10.002     Document Type: Article
Times cited : (13)

References (33)
  • 1
    • 0036018639 scopus 로고    scopus 로고
    • More accurate bidiagonal reduction for computing the singular value decomposition
    • Barlow J.L. More accurate bidiagonal reduction for computing the singular value decomposition. SIAM J. Matrix Anal. Appl. 23 3 (2002) 761-798
    • (2002) SIAM J. Matrix Anal. Appl. , vol.23 , Issue.3 , pp. 761-798
    • Barlow, J.L.1
  • 2
    • 84972034208 scopus 로고
    • Greatest common divisor of several polynomials
    • Barnett S. Greatest common divisor of several polynomials. Proc. Cambridge Philos. Soc. (1971) 263-268
    • (1971) Proc. Cambridge Philos. Soc. , pp. 263-268
    • Barnett, S.1
  • 3
    • 0042711330 scopus 로고
    • Greatest common divisor from generalized Sylvester matrices
    • Barnett S. Greatest common divisor from generalized Sylvester matrices. Proc. Cambridge Philos. Soc. 8 (1980) 271-279
    • (1980) Proc. Cambridge Philos. Soc. , vol.8 , pp. 271-279
    • Barnett, S.1
  • 5
    • 0015143623 scopus 로고
    • On Euclid's algorithm and the computation of polynomials greatest common divisors
    • Brown W.S. On Euclid's algorithm and the computation of polynomials greatest common divisors. Journal of the Association for Computer Machinery 18 4 (1971) 478-504
    • (1971) Journal of the Association for Computer Machinery , vol.18 , Issue.4 , pp. 478-504
    • Brown, W.S.1
  • 6
    • 84946063031 scopus 로고
    • An improved algorithm for computing the singular value decomposition
    • Chan T.F. An improved algorithm for computing the singular value decomposition. ACM Trans. Math. Soft. 8 (1982) 72-83
    • (1982) ACM Trans. Math. Soft. , vol.8 , pp. 72-83
    • Chan, T.F.1
  • 7
    • 0029190375 scopus 로고
    • The singular value decomposition for polynomial systems
    • 95, Quebec, Canada
    • R.M. Corless, P.M. Gianni, B.M. Trager, S.M. Watt, The singular value decomposition for polynomial systems, in: Proc. ISSAC '95, Quebec, Canada, 1995, pp. 195-207
    • (1995) Proc. ISSAC , pp. 195-207
    • Corless, R.M.1    Gianni, P.M.2    Trager, B.M.3    Watt, S.M.4
  • 9
    • 27844599241 scopus 로고    scopus 로고
    • Computing greatest common divisors and squarefree decompositions through matrix methods: The parametric and approximate cases
    • Diaz-Toca G.M., and Gonzalez-Vega L. Computing greatest common divisors and squarefree decompositions through matrix methods: The parametric and approximate cases. Linear Algebra and its Applications 412 (2006) 222-246
    • (2006) Linear Algebra and its Applications , vol.412 , pp. 222-246
    • Diaz-Toca, G.M.1    Gonzalez-Vega, L.2
  • 11
    • 0345689664 scopus 로고    scopus 로고
    • Resultant properties of the gcd of many polynomials and a factorisation representation of gcd
    • Fatouros S., and Karcanias N. Resultant properties of the gcd of many polynomials and a factorisation representation of gcd. Int. Journ. Control 76 16 (2003) 1666-1683
    • (2003) Int. Journ. Control , vol.76 , Issue.16 , pp. 1666-1683
    • Fatouros, S.1    Karcanias, N.2
  • 12
    • 38249043588 scopus 로고
    • Rank and null space calculations using matrix decomposition without column interchanges
    • Foster L. Rank and null space calculations using matrix decomposition without column interchanges. Linear Algebra and its Applications 74 (1986) 47-71
    • (1986) Linear Algebra and its Applications , vol.74 , pp. 47-71
    • Foster, L.1
  • 13
    • 0000288016 scopus 로고
    • Calculating the singular values and pseudo-inverse of a matrix
    • Golub G., and Kahan W. Calculating the singular values and pseudo-inverse of a matrix. SIAM J. Num. Anal. Ser. B 2 (1965) 205-224
    • (1965) SIAM J. Num. Anal. Ser. B , vol.2 , pp. 205-224
    • Golub, G.1    Kahan, W.2
  • 16
    • 0003792312 scopus 로고
    • Prentice Hall, Inc., Englewood Cliffs, NJ
    • Kailath T. Linear Systems (1980), Prentice Hall, Inc., Englewood Cliffs, NJ
    • (1980) Linear Systems
    • Kailath, T.1
  • 17
    • 0023451820 scopus 로고
    • Invariance properties and characterisation of the greatest common divisor of a set of polynomials
    • Karcanias N. Invariance properties and characterisation of the greatest common divisor of a set of polynomials. Int. Journ. Control 46 (1987) 1751-1760
    • (1987) Int. Journ. Control , vol.46 , pp. 1751-1760
    • Karcanias, N.1
  • 18
    • 33747069646 scopus 로고    scopus 로고
    • Approximate greatest common divisor of many polynomials, generalised resultants and strength of approximation
    • Karcanias N., Fatouros S., Mitrouli M., and Halikias G. Approximate greatest common divisor of many polynomials, generalised resultants and strength of approximation. Computers & Mathematics with Applications 51 12 (2006) 1817-1830
    • (2006) Computers & Mathematics with Applications , vol.51 , Issue.12 , pp. 1817-1830
    • Karcanias, N.1    Fatouros, S.2    Mitrouli, M.3    Halikias, G.4
  • 20
    • 0028433638 scopus 로고
    • A matrix pencil based numerical method for the computation of the gcd of polynomials
    • Karcanias N., and Mitrouli M. A matrix pencil based numerical method for the computation of the gcd of polynomials. IEEE Trans. Autom. Cont. 39 (1994) 977-981
    • (1994) IEEE Trans. Autom. Cont. , vol.39 , pp. 977-981
    • Karcanias, N.1    Mitrouli, M.2
  • 21
    • 1342275239 scopus 로고    scopus 로고
    • Approximate algebraic computations of algebraic invariants
    • Symbolic Methods in Control Systems Analysis and Design
    • Karcanias N., and Mitrouli M. Approximate algebraic computations of algebraic invariants. Symbolic Methods in Control Systems Analysis and Design. IEE Control Engin. Series vol. 56 (1999) 162-168
    • (1999) IEE Control Engin. Series , vol.56 , pp. 162-168
    • Karcanias, N.1    Mitrouli, M.2
  • 22
    • 0032349813 scopus 로고    scopus 로고
    • On approximate gcds of univariate polynomials
    • Karmarkar N., and Lakshman Y.N. On approximate gcds of univariate polynomials. J. Symbolic Computation 26 6 (1998) 653-666
    • (1998) J. Symbolic Computation , vol.26 , Issue.6 , pp. 653-666
    • Karmarkar, N.1    Lakshman, Y.N.2
  • 23
    • 71549141655 scopus 로고    scopus 로고
    • J. Leventides, N. Karcanias, Genericity, generic system properties and generic values of invariants, Research Report SDCU 047, Control Engineering Centre, City University, London (May 1996)
    • J. Leventides, N. Karcanias, Genericity, generic system properties and generic values of invariants, Research Report SDCU 047, Control Engineering Centre, City University, London (May 1996)
  • 25
    • 0000703062 scopus 로고
    • Computation of the gcd of polynomials using Gaussian transformation and shifting
    • Mitrouli M., and Karcanias N. Computation of the gcd of polynomials using Gaussian transformation and shifting. Int. Journ. Control 58 (1993) 211-228
    • (1993) Int. Journ. Control , vol.58 , pp. 211-228
    • Mitrouli, M.1    Karcanias, N.2
  • 26
    • 38149143588 scopus 로고
    • Approximate gcd and its applications to ill-conditioned algebraic equations
    • Noda M., and Sasaki T. Approximate gcd and its applications to ill-conditioned algebraic equations. Journ. of Comp. and Appl. Math. 38 (1991) 335-351
    • (1991) Journ. of Comp. and Appl. Math. , vol.38 , pp. 335-351
    • Noda, M.1    Sasaki, T.2
  • 27
    • 0015600818 scopus 로고
    • Comparison of algorithms for calculation of g.c.d. of polynomials
    • Pace I.S., and Barnett S. Comparison of algorithms for calculation of g.c.d. of polynomials. Int. Journ. Control 4 2 (1973) 211-216
    • (1973) Int. Journ. Control , vol.4 , Issue.2 , pp. 211-216
    • Pace, I.S.1    Barnett, S.2
  • 28
    • 0033147489 scopus 로고    scopus 로고
    • An algorithm for computing certified approximate gcd of n univariate polynomials
    • Rupprecht D. An algorithm for computing certified approximate gcd of n univariate polynomials. Journ. of Pure and Applied Algebra 139 (1999) 255-284
    • (1999) Journ. of Pure and Applied Algebra , vol.139 , pp. 255-284
    • Rupprecht, D.1
  • 29
    • 38249018339 scopus 로고
    • Partial singular value decomposition algorithm
    • Van Huffel S. Partial singular value decomposition algorithm. Journ. of Comp. and Appl. Math. 33 (1990) 105-112
    • (1990) Journ. of Comp. and Appl. Math. , vol.33 , pp. 105-112
    • Van Huffel, S.1
  • 30
    • 38249035548 scopus 로고
    • An efficient and reliable algorithm for computing the singular subspace of a matrix, associated with its smallest singular values
    • Van Huffel S., and Vandewalle J. An efficient and reliable algorithm for computing the singular subspace of a matrix, associated with its smallest singular values. Journ. of Comp. and Appl. Math. 19 (1987) 313-330
    • (1987) Journ. of Comp. and Appl. Math. , vol.19 , pp. 313-330
    • Van Huffel, S.1    Vandewalle, J.2
  • 33
    • 36448974692 scopus 로고    scopus 로고
    • The approximate gcd of inexact polynomials. Part I: A univariate algorithm
    • Manuscript
    • Z. Zeng, The approximate gcd of inexact polynomials. Part I: A univariate algorithm, Manuscript, 2004
    • (2004)
    • Zeng, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.