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Volumn 2005, Issue , 2005, Pages 309-316

Computing the rank and a small nullspace basis of a polynomial matrix

Author keywords

Linear algebra; Matrix rank; Minimal polynomial basis; Nullspace basis; Polynomial matrix

Indexed keywords

LINEAR ALGEBRA; MATRIX ALGEBRA; NUMBER THEORY; POLYNOMIALS; VECTORS;

EID: 33749575549     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1073884.1073927     Document Type: Conference Paper
Times cited : (26)

References (34)
  • 1
    • 21344493492 scopus 로고
    • A uniform approach for the fast computation of matrix-type Fade approximants
    • July
    • B. Beckermann and G. Labahn. A uniform approach for the fast computation of matrix-type Fade approximants. SIAM J. Matrix Anal. Appl. 15(3):804-823, July 1994.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , Issue.3 , pp. 804-823
    • Beckermann, B.1    Labahn, G.2
  • 2
    • 85071407731 scopus 로고    scopus 로고
    • Normal forms for funeral polynomial matrices
    • RR LIP 2002-1, Laboratoire LIP, NS Lyon, France. To appear
    • B. Beckermann, G. Labahn, and G.Villard. Normal forms for funeral polynomial matrices. RR LIP 2002-1, Laboratoire LIP, NS Lyon, France, 2002. To appear in J. Symb. Comput.
    • (2002) J. Symb. Comput.
    • Beckermann, B.1    Labahn, G.2    Villard, G.3
  • 3
    • 0003100869 scopus 로고
    • An improved algorithm for the computation of Kronecker's canonical form of a singular pencil
    • T. Beelen and P.M. VanDooren. An improved algorithm for the computation of Kronecker's canonical form of a singular pencil. Lin. Alg. Appl., 105:9-65, 1988.
    • (1988) Lin. Alg. Appl. , vol.105 , pp. 9-65
    • Beelen, T.1    VanDooren, P.M.2
  • 4
    • 0043221496 scopus 로고
    • A pencil approach for embedding a polynomial matrix into a unimodular matrix
    • Jan.
    • T. Beelen and P.M. Van Dooren. A pencil approach for embedding a polynomial matrix into a unimodular matrix. SIAM J. Matrix Anal. Appl., 9(1):77-89, Jan. 1988.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , Issue.1 , pp. 77-89
    • Beelen, T.1    Van Dooren, P.M.2
  • 5
    • 0018059393 scopus 로고
    • Greatest common divisors via generalized Sylvester and Bezout matrices
    • R.R. Bitmead, S.Y. Kung, B.D.O. Anderson, and T. Kailath. Greatest common divisors via generalized Sylvester and Bezout matrices. IEEE Trans. Aut. Control., 23(6):1043-1047, 1978.
    • (1978) IEEE Trans. Aut. Control. , vol.23 , Issue.6 , pp. 1043-1047
    • Bitmead, R.R.1    Kung, S.Y.2    Anderson, B.D.O.3    Kailath, T.4
  • 7
    • 85050898498 scopus 로고    scopus 로고
    • Polynomial evaluation and interpolation on special sets of points
    • To appear
    • A. Bostan and E. Schost. Polynomial evaluation and interpolation on special sets of points. To appear in J. Complexity.
    • J. Complexity
    • Bostan, A.1    Schost, E.2
  • 9
    • 34249916280 scopus 로고
    • On fast multiplication of polynomials over arbitrary algebras
    • D.G. Cantor and E. Kaltofen. On fast multiplication of polynomials over arbitrary algebras. Acta Informatica, 28(7):693-701, 1991.
    • (1991) Acta Informatica , vol.28 , Issue.7 , pp. 693-701
    • Cantor, D.G.1    Kaltofen, E.2
  • 11
    • 85023205150 scopus 로고
    • Matrix multiplication via arithmetic progressions
    • D. Coppersmith and S.Winograd. Matrix multiplication via arithmetic progressions. J. of Symb. Comput., 9(3):251-280, 1990.
    • (1990) J. of Symb. Comput. , vol.9 , Issue.3 , pp. 251-280
    • Coppersmith, D.1    Winograd, S.2
  • 12
    • 0000006297 scopus 로고
    • A probabilistic remark on algebraic program testing
    • R. A. DeMillo and R. J. Lipton. A probabilistic remark on algebraic program testing. Inf. Proc. Letters, 7(4):193-195, 1978.
    • (1978) Inf. Proc. Letters , vol.7 , Issue.4 , pp. 193-195
    • DeMillo, R.A.1    Lipton, R.J.2
  • 13
    • 0016508669 scopus 로고
    • Minimal bases of rational vector spaces, with applications to multivariable linear systems
    • G.D. Forney. Minimal bases of rational vector spaces, with applications to multivariable linear systems. SIAM J. Control, 13:493-520, 1975.
    • (1975) SIAM J. Control , vol.13 , pp. 493-520
    • Forney, G.D.1
  • 16
    • 11844283932 scopus 로고    scopus 로고
    • Essentially optimal computation of the inverse of generic polynomial matrices
    • C.-P. Jeannerod and G.Villard. Essentially optimal computation of the inverse of generic polynomial matrices. J. Complexity, 21(1):72-86, 2005.
    • (2005) J. Complexity , vol.21 , Issue.1 , pp. 72-86
    • Jeannerod, C.-P.1    Villard, G.2
  • 18
    • 49249136112 scopus 로고
    • On computing determinants without divisions
    • ACM Press, July
    • E. Kaltofen. On computing determinants without divisions. In Proc. ISSAC'92, Berkeley, California USA, pages 342-349. ACM Press, July 1992.
    • (1992) Proc. ISSAC'92, Berkeley, California USA , pp. 342-349
    • Kaltofen, E.1
  • 20
    • 84968495217 scopus 로고
    • On Wiedemann's method of solving sparse linear systems
    • LNCS 539, Springer Verlag
    • E. Kaltofen and B.D. Saunders. On Wiedemann's method of solving sparse linear systems. In Proc. AAECC-9, LNCS 539, Springer Verlag, pages 29-38, 1991.
    • (1991) Proc. AAECC-9 , pp. 29-38
    • Kaltofen, E.1    Saunders, B.D.2
  • 21
    • 15244346390 scopus 로고    scopus 로고
    • On the complexity of computing determinants
    • E. Kaltofen and G. Villard. On the complexity of computing determinants. Computational Complexity, 13:91-130, 2004.
    • (2004) Computational Complexity , vol.13 , pp. 91-130
    • Kaltofen, E.1    Villard, G.2
  • 23
    • 0028733634 scopus 로고
    • Computation of structural invariants of generalized state-space systems
    • P. Misra, P. Van Dooren, and A. Varga. Computation of structural invariants of generalized state-space systems. Automatica, 30:1921-1936, 1994.
    • (1994) Automatica , vol.30 , pp. 1921-1936
    • Misra, P.1    Van Dooren, P.2    Varga, A.3
  • 24
    • 0038405094 scopus 로고    scopus 로고
    • On lattice reduction for polynomial matrices
    • T. Mulders and A. Storjohann. On lattice reduction for polynomial matrices. J. Symb. Comput., 35(4):377-401, 2003.
    • (2003) J. Symb. Comput. , vol.35 , Issue.4 , pp. 377-401
    • Mulders, T.1    Storjohann, A.2
  • 25
    • 0002416372 scopus 로고    scopus 로고
    • An improved algorithm for the computation of structural invariants of a system pencil and related geometric aspects
    • C.Oarǎ and P. Van Dooren. An improved algorithm for the computation of structural invariants of a system pencil and related geometric aspects. Syst. Cont. Letters, 30:38-48, 1997.
    • (1997) Syst. Cont. Letters , vol.30 , pp. 38-48
    • Oarǎ, C.1    Van Dooren, P.2
  • 26
    • 0015197550 scopus 로고
    • Schnelle Berechnung von Kettenbruchenwicklungen
    • A. Schönhage. Schnelle Berechnung von Kettenbruchenwicklungen. Acta Informatica, 1:139-144, 1971.
    • (1971) Acta Informatica , vol.1 , pp. 139-144
    • Schönhage, A.1
  • 27
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • J.T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. J. ACM, 27:701-717, 1980.
    • (1980) J. ACM , vol.27 , pp. 701-717
    • Schwartz, J.T.1
  • 28
    • 0003909785 scopus 로고    scopus 로고
    • PhD thesis, Institut für Wissenschaftliches Rechnen, ETH-Zentrum, Zurich, Switzerland, November
    • A. Storjohann. Algorithms for Matrix Canonical Forms. PhD thesis, Institut für Wissenschaftliches Rechnen, ETH-Zentrum, Zurich, Switzerland, November 2000.
    • (2000) Algorithms for Matrix Canonical Forms
    • Storjohann, A.1
  • 30
    • 0042706308 scopus 로고    scopus 로고
    • High-order lifting and integrality certification
    • A. Storjohann. High-order lifting and integrality certification. Journal of Symbolic Computation, 36(3-4) :613-648, 2003.
    • (2003) Journal of Symbolic Computation , vol.36 , Issue.3-4 , pp. 613-648
    • Storjohann, A.1
  • 33
    • 0030658654 scopus 로고    scopus 로고
    • Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems
    • ACM Press, July
    • G.Villard. Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems. In Proc. ISSAC'97, Maui, Hawaii, USA, pages 32-39. ACM Press, July 1997.
    • (1997) Proc. ISSAC'97, Maui, Hawaii, USA , pp. 32-39
    • Villard, G.1
  • 34
    • 84925463455 scopus 로고
    • Probabilistic algorithms for sparse polynomials
    • LNCS 72, Springer Verlag
    • R.E. Zippel. Probabilistic algorithms for sparse polynomials. In Proc. EUROSAM, LNCS 72, Springer Verlag, pages 216-226, 1979.
    • (1979) Proc. EUROSAM , pp. 216-226
    • Zippel, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.