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Volumn 26, Issue 3, 2005, Pages 810-829

Orthogonal rational functions and structured matrices

Author keywords

Diagonal plus semiseparable matrices; Inverse eigenvalue problems; Orthogonal rational functions; Recurrence relation; Structured matrices

Indexed keywords

COMPUTATIONAL COMPLEXITY; EIGENVALUES AND EIGENFUNCTIONS; INTERPOLATION; INVERSE PROBLEMS; MATRIX ALGEBRA; PROBLEM SOLVING; THEOREM PROVING;

EID: 22944448381     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479803444454     Document Type: Article
Times cited : (26)

References (39)
  • 1
    • 22944463605 scopus 로고
    • 2) reduction algorithms for the construction of a band matrix from spectral data
    • 2) reduction algorithms for the construction of a band matrix from spectral data, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 426-431.
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 426-431
    • Ammar, G.1    Gragg, W.2
  • 2
    • 0040782369 scopus 로고
    • Constructing a unitary Hessenberg matrix from spectral data
    • 1 and Parallel Algorithms, G. Golub and P. Van Dooren, eds., Springer-Verlag, Berlin
    • 1 and Parallel Algorithms, G. Golub and P. Van Dooren, eds., NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci. 70, Springer-Verlag, Berlin, 1991, pp. 385-395.
    • (1991) NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci. , vol.70 , pp. 385-395
    • Ammar, G.1    Gragg, W.2    Reichel, L.3
  • 3
    • 0001050004 scopus 로고
    • i, j = 0 for j > i + p
    • i, j = 0 for j > i + p, Math. Scand., 7 (1959), pp. 57-60.
    • (1959) Math. Scand. , vol.7 , pp. 57-60
    • Asplund, E.1
  • 4
    • 11144294629 scopus 로고    scopus 로고
    • QR-like algorithms for generalized semiseparable matrices
    • Dipartimento di Matematica, Università di Pisa, Pisa, Italy
    • D. A. BINI, L. GEMIGNANI, AND V. Y. PAN, QR-like Algorithms for Generalized Semiseparable Matrices, Technical Report 1470, Dipartimento di Matematica, Università di Pisa, Pisa, Italy, 2003.
    • (2003) Technical Report , vol.1470
    • Bini, D.A.1    Gemignani, L.2    Pan, V.Y.3
  • 5
    • 0000964853 scopus 로고
    • A survey of matrix inverse eigenvalue problems
    • D. BOLEY AND G. GOLUB, A survey of matrix inverse eigenvalue problems, Inverse Problems, 3 (1987), pp. 595-622.
    • (1987) Inverse Problems , vol.3 , pp. 595-622
    • Boley, D.1    Golub, G.2
  • 6
    • 0022673797 scopus 로고
    • Padé techniques for model reduction in linear system theory: A survey
    • A. BULTHEEL AND M. VAN BAREL, Padé techniques for model reduction in linear system theory: A survey, J. Comput. Appl. Math., 14 (1986), pp. 401-438.
    • (1986) J. Comput. Appl. Math. , vol.14 , pp. 401-438
    • Bultheel, A.1    Van Barel, M.2
  • 7
    • 0034282372 scopus 로고    scopus 로고
    • Rational approximation in linear systems and control
    • A. BULTHEEL AND B. DE MOOR, Rational approximation in linear systems and control, J. Comput. Appl. Math., 121 (2000), pp. 355-378.
    • (2000) J. Comput. Appl. Math. , vol.121 , pp. 355-378
    • Bultheel, A.1    De Moor, B.2
  • 11
    • 21844489079 scopus 로고
    • Vector orthogonal polynomials and least squares approximation
    • A. BULTHEEL AND M. VAN BAREL, Vector orthogonal polynomials and least squares approximation, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 863-885.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 863-885
    • Bultheel, A.1    Van Barel, M.2
  • 12
    • 22744448835 scopus 로고    scopus 로고
    • A fast and stable solver for recursively semi-separable systems of linear equations
    • Structured Matrices in Mathematics, Computer Science, and Engineering, II (Boulder, CO, 1999), AMS, Providence, RI
    • S. CHANDRASEKARAN AND M. GU, A fast and stable solver for recursively semi-separable systems of linear equations, in Structured Matrices in Mathematics, Computer Science, and Engineering, II (Boulder, CO, 1999), Contemp. Math. 281, AMS, Providence, RI, 2001, pp. 39-53.
    • (2001) Contemp. Math. , vol.281 , pp. 39-53
    • Chandrasekaran, S.1    Gu, M.2
  • 13
    • 0019551389 scopus 로고
    • On the role of the Nevanlinna-pick problem in circuit and system theory
    • P. DELSARTE, Y. GENIN, AND Y. KAMP, On the role of the Nevanlinna-Pick problem in circuit and system theory, Internat. J. Circuit Theory Appl., 9 (1981), pp. 177-187.
    • (1981) Internat. J. Circuit Theory Appl. , vol.9 , pp. 177-187
    • Delsarte, P.1    Genin, Y.2    Kamp, Y.3
  • 14
    • 0032063701 scopus 로고    scopus 로고
    • A look-ahead block Schur algorithm for diagonal plus semiseparable matrices
    • Y. EIDELMAN AND I. GOHBERG, A look-ahead block Schur algorithm for diagonal plus semiseparable matrices, Comput. Math. Appl., 35 (1998), pp. 25-34.
    • (1998) Comput. Math. Appl. , vol.35 , pp. 25-34
    • Eidelman, Y.1    Gohberg, I.2
  • 15
    • 0000149521 scopus 로고
    • Updating and downdating of orthogonal polynomials with data fitting applications
    • S. ELHAY, G. GOLUB, AND J. KAUTSKY, Updating and downdating of orthogonal polynomials with data fitting applications, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 327-353.
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 327-353
    • Elhay, S.1    Golub, G.2    Kautsky, J.3
  • 16
    • 0013293393 scopus 로고    scopus 로고
    • A Lanczos-type algorithm for the QR factorization of regular Cauchy matrices
    • D. FASINO AND L. GEMIGNANI, A Lanczos-type algorithm for the QR factorization of regular Cauchy matrices, Numer. Linear Algebra Appl., 9 (2002), pp. 305-319.
    • (2002) Numer. Linear Algebra Appl. , vol.9 , pp. 305-319
    • Fasino, D.1    Gemignani, L.2
  • 17
    • 22944456474 scopus 로고    scopus 로고
    • A Lanczos-type algorithm for the QR factorization of Cauchy-like matrices
    • Fast Algorithms for Structured Matrices: Theory and Applications, V. Olshevsky, ed., AMS, Providence, RI
    • D. FASINO AND L. GEMIGNANI, A Lanczos-type algorithm for the QR factorization of Cauchy-like matrices, in Fast Algorithms for Structured Matrices: Theory and Applications, Contemp. Math. 323, V. Olshevsky, ed., AMS, Providence, RI, 2003, pp. 91-104.
    • (2003) Contemp. Math. , vol.323 , pp. 91-104
    • Fasino, D.1    Gemignani, L.2
  • 18
    • 4043086344 scopus 로고    scopus 로고
    • Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices
    • D. FASINO AND L. GEMIGNANI, Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices, Numer. Algorithms, 34 (2003), pp. 313-324.
    • (2003) Numer. Algorithms , vol.34 , pp. 313-324
    • Fasino, D.1    Gemignani, L.2
  • 19
    • 0006327956 scopus 로고
    • How to generate unknown orthogonal polynomials out of known orthogonal polynomials
    • B. FISCHER AND G. GOLUB, How to generate unknown orthogonal polynomials out of known orthogonal polynomials, J. Comput. Appl. Math., 43 (1992), pp. 99-115.
    • (1992) J. Comput. Appl. Math. , vol.43 , pp. 99-115
    • Fischer, B.1    Golub, G.2
  • 20
    • 0001183454 scopus 로고
    • Sur les matrices complètement non négatives et oscillatoires
    • F. R. GANTMACHER AND M. G. KREIN, Sur les matrices complètement non négatives et oscillatoires, Compositio Math., 4 (1937), pp. 445-470.
    • (1937) Compositio Math. , vol.4 , pp. 445-470
    • Gantmacher, F.R.1    Krein, M.G.2
  • 21
    • 0035417529 scopus 로고    scopus 로고
    • The use of rational functions in numerical quadrature
    • W. GAUTSCHI, The use of rational functions in numerical quadrature, J. Comput. Appl. Math., 133 (2001), pp. 111-126.
    • (2001) J. Comput. Appl. Math. , vol.133 , pp. 111-126
    • Gautschi, W.1
  • 22
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • G. H. GOLUB AND J. H. WELSCH, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), pp. 221-230.
    • (1969) Math. Comp. , vol.23 , pp. 221-230
    • Golub, G.H.1    Welsch, J.H.2
  • 23
    • 0000996134 scopus 로고
    • On the partial realization problem
    • W. GRAGG AND A. LINDQUIST, On the partial realization problem, Linear Algebra Appl., 50 (1983), pp. 277-319.
    • (1983) Linear Algebra Appl. , vol.50 , pp. 277-319
    • Gragg, W.1    Lindquist, A.2
  • 24
    • 0001190030 scopus 로고
    • The numerically stable reconstruction of Jacobi matrices from spectral data
    • W. B. GRAGG AND W. J. HARROD, The numerically stable reconstruction of Jacobi matrices from spectral data, Numer. Math., 44 (1984), pp. 317-335.
    • (1984) Numer. Math. , vol.44 , pp. 317-335
    • Gragg, W.B.1    Harrod, W.J.2
  • 26
    • 0031460710 scopus 로고    scopus 로고
    • Linear complexity algorithm for semiseparable matrices
    • I. KOLTRACHT, Linear complexity algorithm for semiseparable matrices, Integral Equations Operator Theory, 29 (1997), pp. 313-319.
    • (1997) Integral Equations Operator Theory , vol.29 , pp. 313-319
    • Koltracht, I.1
  • 27
    • 0031116933 scopus 로고    scopus 로고
    • A unifying construction of orthonormal bases for system identification
    • B. NINNESS AND F. GUSTAFSSON, A unifying construction of orthonormal bases for system identification, IEEE Trans. Automat. Control, 42 (1997), pp. 515-521.
    • (1997) IEEE Trans. Automat. Control , vol.42 , pp. 515-521
    • Ninness, B.1    Gustafsson, F.2
  • 28
    • 84887444936 scopus 로고    scopus 로고
    • Polynomial and rational evaluation and interpolation (with structured matrices)
    • Automata, Languages and Programming, Springer-Verag, Berlin
    • V. OLSHEVSKY AND V. PAN, Polynomial and rational evaluation and interpolation (with structured matrices), in Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1644, Springer-Verag, Berlin, 1999, pp. 585-594.
    • (1999) Lecture Notes in Comput. Sci. , vol.1644 , pp. 585-594
    • Olshevsky, V.1    Pan, V.2
  • 29
    • 0000509093 scopus 로고
    • Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation
    • L. REICHEL, Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 552-564.
    • (1991) SIAM J. Matrix Anal. Appl. , vol.12 , pp. 552-564
    • Reichel, L.1
  • 30
    • 0013181076 scopus 로고
    • Construction of polynomials that are orthogonal with respect to a discrete bilinear form
    • L. REICHEL, Construction of polynomials that are orthogonal with respect to a discrete bilinear form, Adv. Comput. Math., 1 (1993), pp. 241-258.
    • (1993) Adv. Comput. Math. , vol.1 , pp. 241-258
    • Reichel, L.1
  • 31
    • 84966200624 scopus 로고
    • Discrete least squares approximation by trigonometric polynomials
    • L. REICHEL, G. AMMAR, AND W. GRAGG, Discrete least squares approximation by trigonometric polynomials, Math. Comp., 57 (1991), pp. 273-289.
    • (1991) Math. Comp. , vol.57 , pp. 273-289
    • Reichel, L.1    Ammar, G.2    Gragg, W.3
  • 33
    • 0039715520 scopus 로고
    • On Jacobi rotation patterns
    • in Experimental Arithmetic, High Speed Computing and Mathematics, AMS, Providence, RI
    • H. RUTISHAUSER, On Jacobi rotation patterns, in Experimental Arithmetic, High Speed Computing and Mathematics, Proc. Sympos. Appl. Math. 15, AMS, Providence, RI, 1963, pp. 219-239.
    • (1963) Proc. Sympos. Appl. Math. , vol.15 , pp. 219-239
    • Rutishauser, H.1
  • 34
    • 38249017528 scopus 로고
    • A new approach to the rational interpolation problem: The vector case
    • M. VAN BAREL AND A. BULTHEEL, A new approach to the rational interpolation problem: The vector case., J. Comput. Appl. Math., 33 (1990), pp. 331-346.
    • (1990) J. Comput. Appl. Math. , vol.33 , pp. 331-346
    • Van Barel, M.1    Bultheel, A.2
  • 35
    • 21144472523 scopus 로고
    • A parallel algorithm for discrete least squares rational approximation
    • M. VAN BAREL AND A. BULTHEEL, A parallel algorithm for discrete least squares rational approximation, Numer. Math., 63 (1992), pp. 99-121.
    • (1992) Numer. Math. , vol.63 , pp. 99-121
    • Van Barel, M.1    Bultheel, A.2
  • 36
    • 0028423962 scopus 로고
    • Discrete linearized least-squares rational approximation on the unit circle
    • M. VAN BAREL AND A. BULTHEEL, Discrete linearized least-squares rational approximation on the unit circle, J. Comput. Appl. Math., 50 (1994), pp. 545-563.
    • (1994) J. Comput. Appl. Math. , vol.50 , pp. 545-563
    • Van Barel, M.1    Bultheel, A.2
  • 37
    • 0001844098 scopus 로고
    • Orthonormal polynomial vectors and least squares approximation for a discrete inner product
    • M. VAN BAREL AND A. BULTHEEL, Orthonormal polynomial vectors and least squares approximation for a discrete inner product, Electron. Trans. Numer. Anal., 3 (1995), pp. 1-23.
    • (1995) Electron. Trans. Numer. Anal. , vol.3 , pp. 1-23
    • Van Barel, M.1    Bultheel, A.2
  • 38
    • 1442314109 scopus 로고    scopus 로고
    • Two fast algorithms for solving diagonal-plus-semiseparable linear systems, 3
    • E. VAN CAMP, N. MASTRONARDI, AND M. VAN BAREL, Two fast algorithms for solving diagonal-plus-semiseparable linear systems, 3. Comput. Appl. Math., 164-165 (2004), pp. 731-747.
    • (2004) Comput. Appl. Math. , vol.164-165 , pp. 731-747
    • Van Camp, E.1    Mastronardi, N.2    Van Barel, M.3
  • 39
    • 11144351583 scopus 로고    scopus 로고
    • An implicit QR algorithm for semiseparable matrices to compute the eigendecomposition of symmetric matrices
    • to appear
    • R. VANDEBRIL, M. VAN BAREL, AND N. MASTRONARDI, An implicit QR algorithm for semiseparable matrices to compute the eigendecomposition of symmetric matrices, Numer. Linear Algebra Appl., to appear.
    • Numer. Linear Algebra Appl.
    • Vandebril, R.1    Van Barel, M.2    Mastronardi, N.3


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