메뉴 건너뛰기




Volumn 22, Issue 1, 2000, Pages 114-144

Fraction-free computation of matrix rational interpolants and matrix GCDs

Author keywords

Fraction free arithmetic; Hermite Pad approximant; Simultaneous Pad approximant; Striped Krylov matrices

Indexed keywords


EID: 0034353665     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479897326912     Document Type: Article
Times cited : (60)

References (55)
  • 2
    • 84968497774 scopus 로고
    • Sylvester's identity and multistep integer-preserving Gaussian elimination
    • E. BAREISS, Sylvester's identity and multistep integer-preserving Gaussian elimination, Math. Comp., 22 (1968), pp. 565-578.
    • (1968) Math. Comp. , vol.22 , pp. 565-578
    • Bareiss, E.1
  • 4
    • 38249018131 scopus 로고
    • The structure of the singular solution table of the M-Padé approximation problem
    • B. BECKERMANN, The structure of the singular solution table of the M-Padé approximation problem, J. Comput. Appl. Math., 32 (1990), pp. 3-15.
    • (1990) J. Comput. Appl. Math. , vol.32 , pp. 3-15
    • Beckermann, B.1
  • 5
    • 38249011670 scopus 로고
    • A reliable method for computing M-Padé approximants on arbitrary staircases
    • B. BECKERMANN, A reliable method for computing M-Padé approximants on arbitrary staircases, J. Comput. Appl. Math., 40 (1992), pp. 19-42.
    • (1992) J. Comput. Appl. Math. , vol.40 , pp. 19-42
    • Beckermann, B.1
  • 6
    • 21344435014 scopus 로고    scopus 로고
    • The stable computation of formal orthogonal polynomials
    • B. BECKERMANN, The stable computation of formal orthogonal polynomials, Numer. Algorithms, 11 (1996), pp. 1-23.
    • (1996) Numer. Algorithms , vol.11 , pp. 1-23
    • Beckermann, B.1
  • 7
    • 0001217669 scopus 로고
    • A uniform approach for Hermite Padé and simultaneous Padé approximants and their matrix generalizations
    • B. BECKERMANN AND G. LABAHN, A uniform approach for Hermite Padé and simultaneous Padé approximants and their matrix generalizations, Numer. Algorithms, 3 (1992), pp. 45-54.
    • (1992) Numer. Algorithms , vol.3 , pp. 45-54
    • Beckermann, B.1    Labahn, G.2
  • 8
    • 21344493492 scopus 로고
    • A uniform approach for the fast, computation of matrix-type Padé approximants
    • B. BECKERMANN AND G. LABAHN, A uniform approach for the fast, computation of matrix-type Padé approximants, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 804-823.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 804-823
    • Beckermann, B.1    Labahn, G.2
  • 9
    • 0030834915 scopus 로고    scopus 로고
    • Recursiveness in matrix rational interpolation problems
    • B. BECKERMANN AND G. LABAHN, Recursiveness in matrix rational interpolation problems, J. Comput. Appl. Math., 77 (1997), pp. 5-34.
    • (1997) J. Comput. Appl. Math. , vol.77 , pp. 5-34
    • Beckermann, B.1    Labahn, G.2
  • 10
    • 0030653019 scopus 로고    scopus 로고
    • Fraction-free Computation of Matrix Padé Systems
    • Maui, HI, ACM Press, New York
    • B. BECKERMANN, S. CABAY, AND G. LABAHN, Fraction-free Computation of Matrix Padé Systems, in Proceedings of ISSAC'97, Maui, HI, ACM Press, New York, 1997, pp. 125-132.
    • (1997) Proceedings of ISSAC'97 , pp. 125-132
    • Beckermann, B.1    Cabay, S.2    Labahn, G.3
  • 11
    • 0007174934 scopus 로고    scopus 로고
    • Shifted Normal Forms of Polynomial Matrices
    • Vancouver, BC, ACM Press, New York
    • B. BECKERMANN, G. LABAHN, AND G. VILLARD, Shifted Normal Forms of Polynomial Matrices, in Proceedings of ISSAC'99, Vancouver, BC, ACM Press, New York, 1999, pp. 189-196.
    • (1999) Proceedings of ISSAC'99 , pp. 189-196
    • Beckermann, B.1    Labahn, G.2    Villard, G.3
  • 13
    • 0000839562 scopus 로고
    • Stability analysis of a general Toeplitz systems solver
    • A.W. BOJANCZYK, R.P. BRENT, AND F.R. DE HOOG, Stability analysis of a general Toeplitz systems solver, Numer. Algorithms, 10 (1995), pp. 225-244.
    • (1995) Numer. Algorithms , vol.10 , pp. 225-244
    • Bojanczyk, A.W.1    Brent, R.P.2    De Hoog, F.R.3
  • 14
    • 21844504467 scopus 로고
    • On the stability of the Bareiss and related Toeplitz factorization algorithms
    • A.W. BOJANCZYK, R.P. BRENT, F.R. DE HOOG, AND D.R. SWEET, On the stability of the Bareiss and related Toeplitz factorization algorithms, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 40-57.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 40-57
    • Bojanczyk, A.W.1    Brent, R.P.2    De Hoog, F.R.3    Sweet, D.R.4
  • 15
    • 84983014125 scopus 로고
    • Fast solution of Toeplitz systems of equations and computation of Padé approximants
    • R. BRENT, F.G. GUSTAVSON, AND D.Y. Y. YUN, Fast solution of Toeplitz systems of equations and computation of Padé approximants, J. Algorithms, 1 (1980), pp. 259-295.
    • (1980) J. Algorithms , vol.1 , pp. 259-295
    • Brent, R.1    Gustavson, F.G.2    Yun, D.Y.Y.3
  • 16
    • 0015141743 scopus 로고
    • On Euclid's algorithm and the theory of subresultants
    • W. BROWN AND J.F. TRAUB, On Euclid's algorithm and the theory of subresultants, J. ACM, 18 (1971), pp. 505-514.
    • (1971) J. ACM , vol.18 , pp. 505-514
    • Brown, W.1    Traub, J.F.2
  • 17
    • 0007241686 scopus 로고
    • A matrix Euclidean algorithm and the matrix minimal Padé approximation problem
    • C. Brezinski, ed., North-Holland, Amsterdam
    • A. BULTHEEL AND M. VAN BAREL, A matrix Euclidean algorithm and the matrix minimal Padé approximation problem, in Continued Fractions and Padé Approximants, C. Brezinski, ed., North-Holland, Amsterdam, pp. 11-51, 1990.
    • (1990) Continued Fractions and Padé Approximants , pp. 11-51
    • Bultheel, A.1    Van Barel, M.2
  • 18
    • 0022663029 scopus 로고
    • Algebraic computations of scaled Padé fractions
    • S. CABAY AND D.K. CHOI, Algebraic computations of scaled Padé fractions, SIAM J. Comput., 15 (1986), pp. 243-270.
    • (1986) SIAM J. Comput. , vol.15 , pp. 243-270
    • Cabay, S.1    Choi, D.K.2
  • 19
    • 38249011762 scopus 로고
    • On the theory and computation of non-perfect Padé-Hermite approximants
    • S. CABAY, G. LABAHN, AND B. BECKERMANN, On the theory and computation of non-perfect Padé-Hermite approximants, J. Comput. Appl. Math., 39 (1992), pp. 295-313.
    • (1992) J. Comput. Appl. Math. , vol.39 , pp. 295-313
    • Cabay, S.1    Labahn, G.2    Beckermann, B.3
  • 20
    • 0030551904 scopus 로고    scopus 로고
    • Computation of numerical Padé-Hermite and simultaneous Padé systems II: A weakly stable algorithm
    • S. CABAY, A.R. JONES, AND G. LABAHN, Computation of numerical Padé-Hermite and simultaneous Padé systems II: A weakly stable algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 268-297.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 268-297
    • Cabay, S.1    Jones, A.R.2    Labahn, G.3
  • 21
    • 0001029686 scopus 로고
    • Power series remainder sequences and Padé fractions over an integral domain
    • S. CABAY AND P. KOSSOWSKI, Power series remainder sequences and Padé fractions over an integral domain, J. Symbolic Comput., 10 (1990), pp. 139-163.
    • (1990) J. Symbolic Comput. , vol.10 , pp. 139-163
    • Cabay, S.1    Kossowski, P.2
  • 22
    • 0007306037 scopus 로고
    • A superfast algorithm for multidimensional Padé systems
    • S. CABAY AND G. LABAHN, A superfast algorithm for multidimensional Padé systems, Numer. Algorithms, 2 (1992), pp. 201-224.
    • (1992) Numer. Algorithms , vol.2 , pp. 201-224
    • Cabay, S.1    Labahn, G.2
  • 23
    • 0008476403 scopus 로고
    • A weakly stable algorithm for Padé approximants and the inversion of Hankel matrices
    • S. CABAY AND R. MELESHKO, A weakly stable algorithm for Padé approximants and the inversion of Hankel matrices, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 735-765.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 735-765
    • Cabay, S.1    Meleshko, R.2
  • 25
    • 84945709818 scopus 로고
    • Subresultant and reduced polynomial remainder sequences
    • G. COLLINS, Subresultant and reduced polynomial remainder sequences, J. ACM, 14 (1967), pp. 128-142.
    • (1967) J. ACM , vol.14 , pp. 128-142
    • Collins, G.1
  • 26
    • 0007295314 scopus 로고
    • A comparison of algorithms for the symbolic computation of Padé approximants
    • Proceedings of EUROSAM'84, J. Fitch, ed., Springer-Verlag, Berlin
    • S.R. CZAPOR AND K.O. GEDDES, A comparison of algorithms for the symbolic computation of Padé approximants, in Proceedings of EUROSAM'84, J. Fitch, ed., Lecture Notes in Comput. Sci. 174, Springer-Verlag, Berlin, 1984, pp. 248-259.
    • (1984) Lecture Notes in Comput. Sci. , vol.174 , pp. 248-259
    • Czapor, S.R.1    Geddes, K.O.2
  • 27
    • 21144474045 scopus 로고
    • Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems
    • R.W. FREUND AND H. ZHA, Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems, Linear Algebra Appl., 188/89 (1993), pp. 255-303.
    • (1993) Linear Algebra Appl. , vol.188 , Issue.89 , pp. 255-303
    • Freund, R.W.1    Zha, H.2
  • 28
    • 21144473694 scopus 로고
    • A look-ahead algorithm for the solution of general Hankel systems
    • R.W. FREUND AND H. ZHA, A look-ahead algorithm for the solution of general Hankel systems, Numer. Math., 64 (1993), pp. 295-321.
    • (1993) Numer. Math. , vol.64 , pp. 295-321
    • Freund, R.W.1    Zha, H.2
  • 29
    • 0023427925 scopus 로고
    • An algorithm for a generalization of the Richardson extrapolation process
    • W.F. FORD AND A. SIDI, An algorithm for a generalization of the Richardson extrapolation process, SIAM J. Numer. Anal., 24 (1987), pp. 1212-1232.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1212-1232
    • Ford, W.F.1    Sidi, A.2
  • 31
    • 84968505008 scopus 로고
    • Fast Gaussian elimination with partial pivoting for matrices with displacement structure
    • I. GOHBERG, T. KAILATH, AND V. OLSHEVSKI, Fast Gaussian elimination with partial pivoting for matrices with displacement structure, Math. Comp., 64 (1995), pp. 1557-1567.
    • (1995) Math. Comp. , vol.64 , pp. 1557-1567
    • Gohberg, I.1    Kailath, T.2    Olshevski, V.3
  • 33
    • 0032366597 scopus 로고    scopus 로고
    • Stable and efficient algorithms for structured systems of linear equations
    • M. GU, Stable and efficient algorithms for structured systems of linear equations, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 279-306.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , pp. 279-306
    • Gu, M.1
  • 34
    • 21144475367 scopus 로고
    • Stable row recurrences for the Padé table and generically superfast look-ahead solvers for non-Hermitian Toeplitz systems
    • M.H. GUTKNECHT, Stable row recurrences for the Padé table and generically superfast look-ahead solvers for non-Hermitian Toeplitz systems, Linear Algebra Appl., 188/89 (1993), pp. 351-421.
    • (1993) Linear Algebra Appl. , vol.188 , Issue.89 , pp. 351-421
    • Gutknecht, M.H.1
  • 35
    • 21844522969 scopus 로고
    • Look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz Systems
    • M.H. GUTKNECHT AND M. HOCHBRUCK, Look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz Systems, Numer. Math., 70 (1995), pp. 181-227.
    • (1995) Numer. Math. , vol.70 , pp. 181-227
    • Gutknecht, M.H.1    Hochbruck, M.2
  • 36
    • 0002675246 scopus 로고
    • Algebraic Methods for Toeplitz-like Matrices and Operators
    • Birkhäuser Verlag, Basel, Boston
    • G. HEINIG AND K. ROST, Algebraic Methods for Toeplitz-like Matrices and Operators, Oper. Theory Adv. Appl. 13, Birkhäuser Verlag, Basel, Boston, 1984.
    • (1984) Oper. Theory Adv. Appl. , vol.13
    • Heinig, G.1    Rost, K.2
  • 37
    • 0003792312 scopus 로고
    • Prentice-Hall Englewood Cliffs, NJ
    • T. KAILATH, Linear Systems, Prentice-Hall Englewood Cliffs, NJ, 1980.
    • (1980) Linear Systems
    • Kailath, T.1
  • 40
    • 21144460361 scopus 로고
    • Inversion Components of block Hankel-like matrices
    • G. LABAHN, Inversion Components of block Hankel-like matrices, Linear Algebra Appl., 177 (1992), pp. 7-48.
    • (1992) Linear Algebra Appl. , vol.177 , pp. 7-48
    • Labahn, G.1
  • 41
    • 0024714423 scopus 로고
    • Matrix Padé fractions and their computation
    • G. LABAHN AND S. CABAY, Matrix Padé fractions and their computation, SIAM J. Comput., 18 (1989), pp. 639-657.
    • (1989) SIAM J. Comput. , vol.18 , pp. 639-657
    • Labahn, G.1    Cabay, S.2
  • 42
    • 0025383439 scopus 로고
    • The inverses of block Hankel and block Toeplitz matrices
    • G. LABAHN, D.K. CHOI, AND S. CABAY, The inverses of block Hankel and block Toeplitz matrices, SIAM J. Comput., 19 (1990), pp. 98-123.
    • (1990) SIAM J. Comput. , vol.19 , pp. 98-123
    • Labahn, G.1    Choi, D.K.2    Cabay, S.3
  • 45
    • 0002728552 scopus 로고
    • Perfect systems
    • K. MAHLER, Perfect systems, Composit. Math., 19 (1968), pp. 95-166.
    • (1968) Composit. Math. , vol.19 , pp. 95-166
    • Mahler, K.1
  • 46
    • 0007238911 scopus 로고
    • Quelques Algorithmes de l'Approximation de Padé-Hermite
    • University of Science and Technology at Lille, Lille, France
    • S. PASZKOWSKI, Quelques Algorithmes de l'Approximation de Padé-Hermite, Publication ANO 89, University of Science and Technology at Lille, Lille, France, 1982.
    • (1982) Publication ANO 89
    • Paszkowski, S.1
  • 47
    • 0023378737 scopus 로고
    • Recurrence relations in Padé-Hermite approximation
    • S. PASZKOWSKI, Recurrence relations in Padé-Hermite approximation, J. Comput. Appl. Math., 19 (1987), pp. 99-107.
    • (1987) J. Comput. Appl. Math. , vol.19 , pp. 99-107
    • Paszkowski, S.1
  • 48
    • 0000952650 scopus 로고
    • Hermite Padé approximation: Basic notions and theorems
    • S. PASZKOWSKI, Hermite Padé approximation: Basic notions and theorems, J. Comput. Appl. Math., 32 (1990), pp. 229-236.
    • (1990) J. Comput. Appl. Math. , vol.32 , pp. 229-236
    • Paszkowski, S.1
  • 49
    • 0028443687 scopus 로고
    • Gfun: A Maple package for the manipulation of generating and holonomic functions in one variable
    • B. SALVY AND P. ZIMMERMANN, Gfun: A Maple package for the manipulation of generating and holonomic functions in one variable, ACM Trans. Math. Software, 20 (1994), pp. 163-177.
    • (1994) ACM Trans. Math. Software , vol.20 , pp. 163-177
    • Salvy, B.1    Zimmermann, P.2
  • 50
    • 0001735812 scopus 로고
    • On a generalization of the Richardson extrapolation process
    • A. SIDI, On a generalization of the Richardson extrapolation process, Numer. Math., 57 (1990), pp. 365-377.
    • (1990) Numer. Math. , vol.57 , pp. 365-377
    • Sidi, A.1
  • 51
    • 0007313710 scopus 로고
    • The computation of non-perfect Padé-Hermite approximants
    • M. VAN BAREL AND A. BULTHEEL, The computation of non-perfect Padé-Hermite approximants, Numer. Algorithms, 1 (1991), pp. 285-304.
    • (1991) Numer. Algorithms , vol.1 , pp. 285-304
    • Van Barel, M.1    Bultheel, A.2
  • 52
    • 0000401644 scopus 로고
    • A general module theoretic framework for vector M-Padé and matrix rational interpolation
    • M. VAN BAREL AND A. BULTHEEL, A general module theoretic framework for vector M-Padé and matrix rational interpolation, Numer. Algorithms, 3 (1992), pp. 451-462.
    • (1992) Numer. Algorithms , vol.3 , pp. 451-462
    • Van Barel, M.1    Bultheel, A.2
  • 53
    • 21944441625 scopus 로고    scopus 로고
    • A look-ahead algorithm for the solution of block Toeplitz systems
    • M. VAN BAREL AND A. BULTHEEL, A look-ahead algorithm for the solution of block Toeplitz systems, Linear Algebra Appl., 266 (1997), pp. 291-335.
    • (1997) Linear Algebra Appl. , vol.266 , pp. 291-335
    • Van Barel, M.1    Bultheel, A.2
  • 54
    • 0031281466 scopus 로고    scopus 로고
    • Factorization of differential operators with rational function coefficients
    • M. VAN HOEIJ, Factorization of differential operators with rational function coefficients, J. Symbolic Comput., 24 (1997), pp. 537-561.
    • (1997) J. Symbolic Comput. , vol.24 , pp. 537-561
    • Van Hoeij, M.1
  • 55
    • 0030381773 scopus 로고    scopus 로고
    • Computing Popov and Hermite forms of polynomial matrices
    • Zurich, ACM Press, New York
    • G. VlLLARD, Computing Popov and Hermite forms of polynomial matrices, in Proceedings of ISSAC'96, Zurich, ACM Press, New York, 1996, pp. 250-258.
    • (1996) Proceedings of ISSAC'96 , pp. 250-258
    • Vlllard, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.