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Volumn 285, Issue 1-3, 1998, Pages 229-255

Solution of Toeplitz normal equations by sine transform based preconditioning

Author keywords

Least squares; Normal equations; Preconditioning; Sine transform; Toeplitz matrix

Indexed keywords


EID: 0040716183     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0024-3795(98)10115-5     Document Type: Article
Times cited : (17)

References (32)
  • 1
    • 0003090115 scopus 로고
    • Superfast solution of real positive definite Toeplitz systems
    • G. Ammar, W. Gragg, Superfast solution of real positive definite Toeplitz systems, SIAM J. Matrix Anal. Appl. 9 (1988) 61-76.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 61-76
    • Ammar, G.1    Gragg, W.2
  • 2
    • 0002887353 scopus 로고
    • Spectral and computational properties of band symmetric Toeplitz matrices
    • D. Bini, M. Capovani, Spectral and computational properties of band symmetric Toeplitz matrices, Linear Algebra Appl. 52 (1983) 99-126.
    • (1983) Linear Algebra Appl. , vol.52 , pp. 99-126
    • Bini, D.1    Capovani, M.2
  • 3
    • 0025657332 scopus 로고
    • A new preconditioner for the parallel solution of positive definite Toeplitz systems
    • ACM Press, Crete, Greece
    • D. Bini, F. Di Benedetto, A new preconditioner for the parallel solution of positive definite Toeplitz systems, Proceedings of the Second Annual SPAA, ACM Press, Crete, Greece, 1990, pp. 220-223.
    • (1990) Proceedings of the Second Annual SPAA , pp. 220-223
    • Bini, D.1    Di Benedetto, F.2
  • 4
    • 21844502380 scopus 로고
    • Fast transform based preconditioners for Toeplitz equations
    • E. Boman, I. Koltracht, Fast transform based preconditioners for Toeplitz equations, SIAM J. Matrix Anal. Appl. 16 (1995) 628-645.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 628-645
    • Boman, E.1    Koltracht, I.2
  • 5
    • 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. Stat. Comp. 6 (1985) 349-364.
    • (1985) SIAM J. Sci. Stat. Comp. , vol.6 , pp. 349-364
    • Bunch, J.R.1
  • 6
    • 0000746140 scopus 로고
    • A family of block preconditioners for block systems
    • R.H. Chan, X.Q. Jin, A family of block preconditioners for block systems, SIAM J. Sci. Stat. Comp. 13 (1992) 1218-1235.
    • (1992) SIAM J. Sci. Stat. Comp. , vol.13 , pp. 1218-1235
    • Chan, R.H.1    Jin, X.Q.2
  • 7
    • 0027837097 scopus 로고
    • FFT-based preconditioners for Toeplitz-block least squares problems
    • R.H. Chan, J.G. Nagy, R.J. Plemmons, FFT-based preconditioners for Toeplitz-block least squares problems, SIAM J. Numer. Anal. 30 (1993) 1740-1768.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1740-1768
    • Chan, R.H.1    Nagy, J.G.2    Plemmons, R.J.3
  • 9
    • 0009898160 scopus 로고
    • Displacement preconditioner for Toeplitz least squares iterations
    • R.H. Chan, J.G. Nagy, R.J. Plemmons, Displacement preconditioner for Toeplitz least squares iterations, Elec. Trans. Numer. Anal. 2 (1994) 44-56.
    • (1994) Elec. Trans. Numer. Anal. , vol.2 , pp. 44-56
    • Chan, R.H.1    Nagy, J.G.2    Plemmons, R.J.3
  • 10
    • 38248999546 scopus 로고
    • Toeplitz preconditioners for Hermitian Toeplitz systems
    • R.H. Chan, K.P. Ng, Toeplitz preconditioners for Hermitian Toeplitz systems, Linear Algebra Appl. 190 (1993) 181-208.
    • (1993) Linear Algebra Appl. , vol.190 , pp. 181-208
    • Chan, R.H.1    Ng, K.P.2
  • 11
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods for Toeplitz systems
    • R.H. Chan, M. Ng, Conjugate gradient methods for Toeplitz systems, SIAM Rev. 38 (1996) 427-182.
    • (1996) SIAM Rev. , vol.38 , pp. 427-1182
    • Chan, R.H.1    Ng, M.2
  • 12
    • 21844523518 scopus 로고    scopus 로고
    • Sine transform based preconditioners for symmetric Toeplitz systems
    • R.H. Chan, M. Ng, C.K. Wong, Sine transform based preconditioners for symmetric Toeplitz systems, Linear Algebra Appl. 232 (1996) 237-260.
    • (1996) Linear Algebra Appl. , vol.232 , pp. 237-260
    • Chan, R.H.1    Ng, M.2    Wong, C.K.3
  • 13
    • 0001646777 scopus 로고
    • Toeplitz equations by conjugate gradients with circulant preconditioner
    • R.H. Chan, G. Strang, Toeplitz equations by conjugate gradients with circulant preconditioner, SIAM J. Sci. Stat. Comp. 10 (1989) 104-119.
    • (1989) SIAM J. Sci. Stat. Comp. , vol.10 , pp. 104-119
    • Chan, R.H.1    Strang, G.2
  • 14
    • 0000853646 scopus 로고
    • An optimal circulant preconditioner for Toeplitz systems
    • T. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Stat. Comp. 9 (1988) 766-771.
    • (1988) SIAM J. Sci. Stat. Comp. , vol.9 , pp. 766-771
    • Chan, T.1
  • 15
    • 0000261363 scopus 로고
    • Analysis of preconditioning techniques for ill-conditioned Toeplitz matrices
    • F. Di Benedetto, Analysis of preconditioning techniques for ill-conditioned Toeplitz matrices, SIAM J. Sci. Comp. 16 (1995) 682-697.
    • (1995) SIAM J. Sci. Comp. , vol.16 , pp. 682-697
    • Di Benedetto, F.1
  • 17
    • 0031082706 scopus 로고    scopus 로고
    • Preconditioning of block Toeplitz matrices by sine transforms
    • F. Di Benedetto, Preconditioning of block Toeplitz matrices by sine transforms. SIAM J. Sci. Comp. 18 (1997) 499-515.
    • (1997) SIAM J. Sci. Comp. , vol.18 , pp. 499-515
    • Di Benedetto, F.1
  • 19
    • 84923732006 scopus 로고    scopus 로고
    • A unifying approach to abstract matrix algebra preconditioning
    • to appear
    • F. Di Benedetto, S. Serra Capizzano, A unifying approach to abstract matrix algebra preconditioning, Numer. Math. (to appear).
    • Numer. Math.
    • Di Benedetto, F.1    Serra Capizzano, S.2
  • 20
  • 21
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • M.R. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards 49 (1952) 409-435.
    • (1952) J. Res. Nat. Bur. Standards , vol.49 , pp. 409-435
    • Hestenes, M.R.1    Stiefel, E.2
  • 22
    • 0017500684 scopus 로고
    • A Levinson-type algorithm for two-dimensional Wiener filtering using bivariate Szegö polynomials
    • J.H. Justice, A Levinson-type algorithm for two-dimensional Wiener filtering using bivariate Szegö polynomials, Proc. IEEE 65 (1977) 882-886.
    • (1977) Proc. IEEE , vol.65 , pp. 882-886
    • Justice, J.H.1
  • 23
    • 0000504541 scopus 로고
    • On the spectrum of a family of preconditioned block Toeplitz matrices
    • T.K. Ku, C.C.J. Kuo, On the spectrum of a family of preconditioned block Toeplitz matrices, SIAM J. Sci. Stat. Comp. 13 (1992) 948-966.
    • (1992) SIAM J. Sci. Stat. Comp. , vol.13 , pp. 948-966
    • Ku, T.K.1    Kuo, C.C.J.2
  • 24
    • 21144478031 scopus 로고
    • Spectral properties of preconditioned rational Toeplitz matrices: The nonsymmetric case
    • T.K. Ku, C.C.J. Kuo, Spectral properties of preconditioned rational Toeplitz matrices: The nonsymmetric case, SIAM J. Matrix Anal. Appl. 14 (1993) 521-544.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 521-544
    • Ku, T.K.1    Kuo, C.C.J.2
  • 25
    • 0025419149 scopus 로고
    • Solution and linear estimation of 2-D nearest-neighbor models
    • B.C. Levy, M.B. Adams, A.S. Willsky, Solution and linear estimation of 2-D nearest-neighbor models, Proc. IEEE 78 (1990) 627-641.
    • (1990) Proc. IEEE , vol.78 , pp. 627-641
    • Levy, B.C.1    Adams, M.B.2    Willsky, A.S.3
  • 26
    • 0008770798 scopus 로고
    • A special class of structured matrices constructed with the Kronecker product and its use for difference equations
    • L. Mertens, H. Van de Vel, A special class of structured matrices constructed with the Kronecker product and its use for difference equations, Linear Algebra Appl. 106 (1988) 117-147.
    • (1988) Linear Algebra Appl. , vol.106 , pp. 117-147
    • Mertens, L.1    Van De Vel, H.2
  • 27
    • 0040282415 scopus 로고
    • Iterative image restoration using FFT-based preconditioners
    • University of Illinois, Champaign, Urbana
    • J.G. Nagy, R.J. Plemmons, Iterative image restoration using FFT-based preconditioners, Proceedings of The Allerton Conference, University of Illinois, Champaign, Urbana, 1992.
    • (1992) Proceedings of The Allerton Conference
    • Nagy, J.G.1    Plemmons, R.J.2
  • 28
    • 0000460001 scopus 로고
    • On the distribution of the singular values of Toeplitz matrices
    • S.V. Parter, On the distribution of the singular values of Toeplitz matrices, Linear Algebra Appl. 80 (1986) 115-130.
    • (1986) Linear Algebra Appl. , vol.80 , pp. 115-130
    • Parter, S.V.1
  • 29
    • 0033446353 scopus 로고    scopus 로고
    • Superlinear PCG methods for symmetric Toeplitz systems
    • to appear
    • S. Serra, Superlinear PCG methods for symmetric Toeplitz systems, Math. Comp. (to appear).
    • Math. Comp.
    • Serra, S.1
  • 30
    • 0002716979 scopus 로고
    • CGS: A fast Lanczos-type solver for nonsymmetric linear systems
    • P. Sonneveld, CGS: A fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Stat. Comp. 10 (1989) 115-130.
    • (1989) SIAM J. Sci. Stat. Comp. , vol.10 , pp. 115-130
    • Sonneveld, P.1
  • 31
    • 0040850695 scopus 로고
    • Influence of matrix operations on the distribution of eigenvalues and singular values of Toeplitz matrices
    • E. Tyrtyshnikov, Influence of matrix operations on the distribution of eigenvalues and singular values of Toeplitz matrices, Linear Algebra Appl. 207 (1994) 225-249.
    • (1994) Linear Algebra Appl. , vol.207 , pp. 225-249
    • Tyrtyshnikov, E.1
  • 32
    • 3042570112 scopus 로고    scopus 로고
    • A unifying approach to some old and new theorems on distribution and clustering
    • E. Tyrtyshnikov, A unifying approach to some old and new theorems on distribution and clustering, Linear Algebra Appl. 232 (1996) 1-43.
    • (1996) Linear Algebra Appl. , vol.232 , pp. 1-43
    • Tyrtyshnikov, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.