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Volumn 19, Issue 2, 1998, Pages 279-306

Stable and efficient algorithms for structured systems of linear equations

Author keywords

Displacement equation; Error analysis; Fast algorithm; Toeplitz matrix

Indexed keywords


EID: 0032366597     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479895291273     Document Type: Article
Times cited : (43)

References (28)
  • 2
    • 21844492426 scopus 로고
    • On the use of certain matrix algebras associated with discrete trigonometric transforms in matrix displacement decomposition
    • E. BOZZO AND C. DI FIORE, On the use of certain matrix algebras associated with discrete trigonometric transforms in matrix displacement decomposition, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 312-326.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 312-326
    • Bozzo, E.1    Di Fiore, C.2
  • 3
    • 0000102913 scopus 로고
    • Stability of methods for solving Toeplitz systems of equations
    • J. R. BUNCH, Stability of methods for solving Toeplitz systems of equations, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 349-364.
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 349-364
    • Bunch, J.R.1
  • 4
    • 0026862959 scopus 로고
    • A lookahead Levinson algorithm for general Toeplitz systems
    • T. F. CHAN AND P. C. HANSEN, A lookahead Levinson algorithm for general Toeplitz systems, IEEE Proc. Signal Processing, 40 (1992), pp. 1079-1090.
    • (1992) IEEE Proc. Signal Processing , vol.40 , pp. 1079-1090
    • Chan, T.F.1    Hansen, P.C.2
  • 5
    • 0032343445 scopus 로고    scopus 로고
    • A fast stable solver for nonsymmetric Toeplitz and quasi-Toeplitz systems of linear equations
    • S. CHANDRASEKARAN AND A. H. SAYED, A fast stable solver for nonsymmetric Toeplitz and quasi-Toeplitz systems of linear equations, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 107-139.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , pp. 107-139
    • Chandrasekaran, S.1    Sayed, A.H.2
  • 6
    • 0030519188 scopus 로고    scopus 로고
    • Stabilizing the fast generalized Schur algorithm
    • S. CHANDRASEKARAN AND A. H. SAYED, Stabilizing the fast generalized Schur algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 950-983.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 950-983
    • Chandrasekaran, S.1    Sayed, A.H.2
  • 7
    • 21144451635 scopus 로고
    • Generalized displacement structure for block-Toeplitz, Toeplitz-block, and Toeplitz-derived matrices
    • J. CHUN AND T. KAILATH, Generalized displacement structure for block-Toeplitz, Toeplitz-block, and Toeplitz-derived matrices, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 114-128.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 114-128
    • Chun, J.1    Kailath, T.2
  • 8
    • 0001112325 scopus 로고
    • The numerical stability of Levinson-Durbin algorithm for Toeplitz systems of equations
    • G. CYBENKO, The numerical stability of Levinson-Durbin algorithm for Toeplitz systems of equations, SIAM J. Sci. Statist. Comput., 1 (1980), pp. 303-319.
    • (1980) SIAM J. Sci. Statist. Comput. , vol.1 , pp. 303-319
    • Cybenko, G.1
  • 10
    • 0001883973 scopus 로고
    • Hankel and Loewner matrices
    • M. FIEDLER, Hankel and Loewner matrices, Linear Algebra Appl., 58 (1984), pp. 75-95.
    • (1984) Linear Algebra Appl. , vol.58 , pp. 75-95
    • Fiedler, M.1
  • 11
    • 84968505008 scopus 로고
    • Fast Gaussian elimination with partial pivoting for matrices with displacement structure
    • I. GOHBERG, T. KAILATH, AND V. OLSHEVSKY, Fast Gaussian elimination with partial pivoting for matrices with displacement structure, Math. Comp., 64 (1995), pp. 1557-1576.
    • (1995) Math. Comp. , vol.64 , pp. 1557-1576
    • Gohberg, I.1    Kailath, T.2    Olshevsky, V.3
  • 12
    • 38149147254 scopus 로고
    • Complexity of multiplication with vectors for structured matrices
    • I. GOHBERG AND V. OLSHEVSKY, Complexity of multiplication with vectors for structured matrices, Linear Algebra Appl., 202 (1994), pp. 163-192.
    • (1994) Linear Algebra Appl. , vol.202 , pp. 163-192
    • Gohberg, I.1    Olshevsky, V.2
  • 13
    • 0000536004 scopus 로고
    • Fast algorithm for matrix Nehari problem
    • Systems and Networks: Mathematical Theory and Applications, U. Helmke, R. Mennicken, and J. Sauers, eds., Akademie Verlag, Berlin
    • I. GOHBERG AND V. OLSHEVSKY, Fast algorithm for matrix Nehari problem, in Systems and Networks: Mathematical Theory and Applications, Proc. of the International Symposium MTNS-93, U. Helmke, R. Mennicken, and J. Sauers, eds., Akademie Verlag, Berlin, 2 (1994), pp. 687-690.
    • (1994) Proc. of the International Symposium MTNS-93 , vol.2 , pp. 687-690
    • Gohberg, I.1    Olshevsky, V.2
  • 14
    • 0001926832 scopus 로고
    • Fast state space algorithms for matrix Nehari and Nehari-Takagi interpolation problems
    • I. GOHBERG AND V. OLSHEVSKY, Fast state space algorithms for matrix Nehari and Nehari-Takagi interpolation problems, Integral Equations Oper. Theory, 20 (1994), pp. 44-83.
    • (1994) Integral Equations Oper. Theory , vol.20 , pp. 44-83
    • Gohberg, I.1    Olshevsky, V.2
  • 16
    • 0003787099 scopus 로고
    • Look-Ahead Levinson and Schur Algorithms for Non-Hermitian Toeplitz Systems
    • IPS Supercomputing, ETH-Zürich, Switzerland
    • M. H. GUTKNECHT AND HOCHBRUCK M., Look-Ahead Levinson and Schur Algorithms for Non-Hermitian Toeplitz Systems, IPS Research Report 93-11, IPS Supercomputing, ETH-Zürich, Switzerland, 1993.
    • (1993) IPS Research Report 93-11
    • Gutknecht, M.H.1    Hochbruck, M.2
  • 17
    • 0002638254 scopus 로고
    • Inversion of generalized Cauchy matrices and other classes of structured matrices
    • G. HEINIG, Inversion of generalized Cauchy matrices and other classes of structured matrices, in Linear Algebra in Signal Processing, IMA Vol. Math. Appl., 69 (1994), pp. 95-114.
    • (1994) Linear Algebra in Signal Processing, IMA Vol. Math. Appl. , vol.69 , pp. 95-114
    • Heinig, G.1
  • 18
    • 0000927803 scopus 로고
    • Fast inversion of Toeplitz-plus-Hankel matrices
    • G. HEINIG, P. JANKOWSKI, AND K. ROST, Fast inversion of Toeplitz-plus-Hankel matrices, Numer. Math, 52 (1988), pp. 665-682.
    • (1988) Numer. Math , vol.52 , pp. 665-682
    • Heinig, G.1    Jankowski, P.2    Rost, K.3
  • 19
    • 0002675246 scopus 로고
    • Algebraic methods for Toeplitz-like matrices and operators
    • G. HEINIG AND K. ROST, Algebraic methods for Toeplitz-like matrices and operators, Oper. Theory, 13 (1984), pp. 109-127.
    • (1984) Oper. Theory , vol.13 , pp. 109-127
    • Heinig, G.1    Rost, K.2
  • 21
    • 0017951648 scopus 로고
    • Displacement ranks of matrices and linear equations
    • T. KAILATH, S. KUNG, AND M. MORF, Displacement ranks of matrices and linear equations, J. Math. Anal. Appl., 68 (1979), pp. 395-407.
    • (1979) J. Math. Anal. Appl. , vol.68 , pp. 395-407
    • Kailath, T.1    Kung, S.2    Morf, M.3
  • 23
    • 0000665794 scopus 로고
    • Displacement structure: Theory and applications
    • T. KAILATH AND A. H. SAYED, Displacement structure: Theory and applications, SIAM Rev., 37 (1995), pp. 297-386.
    • (1995) SIAM Rev. , vol.37 , pp. 297-386
    • Kailath, T.1    Sayed, A.H.2
  • 24
    • 84966229708 scopus 로고
    • On computations with dense structured matrices
    • V. PAN, On computations with dense structured matrices, Math. Comp., 55 (1990), pp. 179-190.
    • (1990) Math. Comp. , vol.55 , pp. 179-190
    • Pan, V.1
  • 25
    • 21144466758 scopus 로고
    • The use of pivoting to improve the numerical performance of Toeplitz matrix algorithms
    • D. R. SWEET, The use of pivoting to improve the numerical performance of Toeplitz matrix algorithms, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 468-493.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 468-493
    • Sweet, D.R.1
  • 26
    • 84946574293 scopus 로고
    • Error analysis of a fast partial pivoting method for structured matrices
    • Proc. of SPIE, T. Luk, ed.
    • D. R. SWEET AND R. P. BRENT, Error analysis of a fast partial pivoting method for structured matrices, in Adv. Signal Proc. Algorithms, Proc. of SPIE, T. Luk, ed., 2363 (1995), pp. 266-280.
    • (1995) Adv. Signal Proc. Algorithms , vol.2363 , pp. 266-280
    • Sweet, D.R.1    Brent, R.P.2
  • 27
    • 21144459737 scopus 로고
    • The Prolate matrix
    • J. M. VARAH, The Prolate matrix, Linear Algebra Appl., 187 (1993), pp. 269-278.
    • (1993) Linear Algebra Appl. , vol.187 , pp. 269-278
    • Varah, J.M.1
  • 28
    • 84945709312 scopus 로고
    • Error analysis of direct methods of matrix inversion
    • J. H. WILKINSON, Error analysis of direct methods of matrix inversion, J. Assoc. Comput. Mach., 10 (1961), pp. 281-330.
    • (1961) J. Assoc. Comput. Mach. , vol.10 , pp. 281-330
    • Wilkinson, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.