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Volumn 267, Issue 1-3, 1997, Pages 139-161

The extension of the concept of the generating function to a class of preconditioned Toeplitz matrices

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EID: 0039835885     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0024-3795(97)82204-5     Document Type: Article
Times cited : (19)

References (46)
  • 1
    • 0003083525 scopus 로고
    • On bilinear forms on Gaussian random variables and Toeplitz matrices
    • F. Avram, On bilinear forms on Gaussian random variables and Toeplitz matrices, Probab. Theory Related Fields 79:37-45 (1988).
    • (1988) Probab. Theory Related Fields , vol.79 , pp. 37-45
    • Avram, F.1
  • 3
    • 0000696639 scopus 로고
    • The rate of convergence of the preconditioned conjugate gradient method
    • O. Axelsson and G. Lindskög, The rate of convergence of the preconditioned conjugate gradient method, Numer. Math. 52:499-523 (1986).
    • (1986) Numer. Math. , vol.52 , pp. 499-523
    • Axelsson, O.1    Lindskög, G.2
  • 5
    • 0002887353 scopus 로고
    • Spectral and computational properties of band symmetric Toeplitz matrices
    • D. Bini and M. Capovani, Spectral and computational properties of band symmetric Toeplitz matrices, Linear Algebra Appl. 52/53:99-126 (1983).
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 99-126
    • Bini, D.1    Capovani, M.2
  • 6
    • 0025657332 scopus 로고
    • A new preconditioner for the parallel solution of positive definite Toeplitz linear systems
    • Crete, Greece, July
    • D. Bini and F. Di Benedetto, A new preconditioner for the parallel solution of positive definite Toeplitz linear systems, in Proceedings of the 2nd SPAA Conference, Crete, Greece, July 1990, pp. 220-223.
    • (1990) Proceedings of the 2nd SPAA Conference , pp. 220-223
    • Bini, D.1    Di Benedetto, F.2
  • 7
    • 21144460588 scopus 로고
    • On a matrix algebra related to the discrete Hartley transform
    • D. Bini and P. Favati, On a matrix algebra related to the discrete Hartley transform, SIAM J. Matrix Anal. Appl. 14:500-507 (1993).
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 500-507
    • Bini, D.1    Favati, P.2
  • 8
    • 0001090278 scopus 로고
    • Toeplitz preconditioners for Toeplitz systems with nonnegative generating functions
    • R. H. Chan, Toeplitz preconditioners for Toeplitz systems with nonnegative generating functions, IMA J. Numer. Anal., 11:333-345 (1991).
    • (1991) IMA J. Numer. Anal. , vol.11 , pp. 333-345
    • Chan, R.H.1
  • 9
    • 0001591858 scopus 로고    scopus 로고
    • Toeplitz-circulant preconditioners for Toeplitz systems and their applications to queueing network with batch arrivals
    • R. H. Chan and W. Ching, Toeplitz-circulant preconditioners for Toeplitz systems and their applications to queueing network with batch arrivals, SIAM J. Sci. Comput. 17:762-772 (1996).
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 762-772
    • Chan, R.H.1    Ching, W.2
  • 11
    • 0001646777 scopus 로고
    • Toeplitz equations by conjugate gradients with circulant preconditioner
    • R. H. Chan and G. Strang, Toeplitz equations by conjugate gradients with circulant preconditioner, SIAM J. Sci. Statist. Comput. 10:104-119 (1989).
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 104-119
    • Chan, R.H.1    Strang, G.2
  • 12
    • 0001589542 scopus 로고    scopus 로고
    • Fast band-Toeplitz preconditioners for Hermitian Toeplitz systems
    • R. H. Chan and P. Tang, Fast band-Toeplitz preconditioners for Hermitian Toeplitz systems, SIAM J. Sci. Comput. 15:164-171.
    • SIAM J. Sci. Comput. , vol.15 , pp. 164-171
    • Chan, R.H.1    Tang, P.2
  • 13
    • 0000853646 scopus 로고
    • An optimal circulant preconditioner for Toeplitz systems
    • T. F. Chan, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Statist. Comput. 9:766-771 (1988).
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 766-771
    • Chan, T.F.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. Comput. 16:682-697 (1995).
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 682-697
    • Di Benedetto, F.1
  • 17
    • 0003267923 scopus 로고
    • Convolution equations and projection methods for their solution
    • Amer. Math. Soc., Providence
    • I. Gohberg and I. Feldman, Convolution Equations and Projection Methods for Their Solution, Transl. Math. Monogr. 41, Amer. Math. Soc., Providence, 1974.
    • (1974) Transl. Math. Monogr. , vol.41
    • Gohberg, I.1    Feldman, I.2
  • 21
    • 0000405592 scopus 로고
    • On the extreme eigenvalues of certain Hermitian forms
    • M. Kac, W. Murdoch, and G. Szegö, On the extreme eigenvalues of certain Hermitian forms, J. Rational Mech. Anal., 13:767-800 (1953).
    • (1953) J. Rational Mech. Anal. , vol.13 , pp. 767-800
    • Kac, M.1    Murdoch, W.2    Szegö, G.3
  • 22
    • 0039331372 scopus 로고
    • On some new Banach algebras and Wiener-Levy theorems for Fourier Series and integrals
    • M. G. Krein, On some new Banach algebras and Wiener-Levy theorems for Fourier Series and integrals, Amer. Math. Soc. Transl. 93:177-199 (1970).
    • (1970) Amer. Math. Soc. Transl. , vol.93 , pp. 177-199
    • Krein, M.G.1
  • 24
    • 84968504291 scopus 로고    scopus 로고
    • Extreme eignevalues of Toeplitz forms and applications to elliptic difference equations
    • S. V. Parter, Extreme eignevalues of Toeplitz forms and applications to elliptic difference equations, Trans. Amer. Math. Soc. 99:153-162 (1996).
    • (1996) Trans. Amer. Math. Soc. , vol.99 , pp. 153-162
    • Parter, S.V.1
  • 25
    • 0000460001 scopus 로고
    • On the distribution of singular values of Toeplitz matrices
    • S. V. Parter, On the distribution of singular values of Toeplitz matrices, Lin. Algebra Appl. 80:115-130 (1986).
    • (1986) Lin. Algebra Appl. , vol.80 , pp. 115-130
    • Parter, S.V.1
  • 26
    • 0041110736 scopus 로고    scopus 로고
    • Remarks on the extreme eigenvalues of Toeplitz matrices
    • M. Pourahamadi, Remarks on the extreme eigenvalues of Toeplitz matrices, Internat. J. Math. Math. Sci. 11:23-26.
    • Internat. J. Math. Math. Sci. , vol.11 , pp. 23-26
    • Pourahamadi, M.1
  • 27
    • 20744448636 scopus 로고
    • Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems
    • S. Serra, Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems, BIT 34:579-594 (1994).
    • (1994) BIT , vol.34 , pp. 579-594
    • Serra, S.1
  • 28
    • 0009257011 scopus 로고
    • Conditioning and solution of Hermitian (block) Toeplitz systems by means of preconditioned conjugate gradient methods
    • (F. Luk, Ed.), San Diego, July
    • S. Serra, Conditioning and solution of Hermitian (block) Toeplitz systems by means of preconditioned conjugate gradient methods, in Proceedings in Advanced Signal Processing Algorithms, Architectures, and Implementations - SPIE conference (F. Luk, Ed.), San Diego, July 1995, pp. 326-337.
    • (1995) Proceedings in Advanced Signal Processing Algorithms, Architectures, and Implementations - SPIE Conference , pp. 326-337
    • Serra, S.1
  • 29
    • 0030520048 scopus 로고    scopus 로고
    • Preconditioning strategies for Hermitian Toeplitz systems with nondefinite generating functions
    • S. Serra, Preconditioning strategies for Hermitian Toeplitz systems with nondefinite generating functions, SIAM J. Matrix Anal. Appl. 17(4):1007-1019, (1996).
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.4 , pp. 1007-1019
    • Serra, S.1
  • 30
    • 0041494509 scopus 로고    scopus 로고
    • On the extreme eigenvalues of Hermitian (block) Toeplitz matrices
    • in press
    • S. Serra, On the extreme eigenvalues of Hermitian (block) Toeplitz matrices, Linear Algebra Appl., in press.
    • Linear Algebra Appl.
    • Serra, S.1
  • 31
    • 2542631361 scopus 로고    scopus 로고
    • 1 functions with several minima (maxima)
    • 1 functions with several minima (maxima), BIT, 36:135-142 (1996).
    • (1996) BIT , vol.36 , pp. 135-142
    • Serra, S.1
  • 32
    • 0039758357 scopus 로고    scopus 로고
    • Optimal, quasi-optimal and superlinear preconditioned for asymptotically ill-conditioned positive definite Toeplitz matrices
    • S. Serra, Optimal, quasi-optimal and superlinear preconditioned for asymptotically ill-conditioned positive definite Toeplitz matrices, Math. Comp., 66:651-665 (1997).
    • (1997) Math. Comp. , vol.66 , pp. 651-665
    • Serra, S.1
  • 33
    • 0345908364 scopus 로고    scopus 로고
    • Sulle proprietà spettrali di matrici precondizionate di Toeplitz
    • S. Serra, Sulle proprietà spettrali di matrici precondizionate di Toeplitz, Boll. Un. Mat. Ital., 11-7:463-483 (1997).
    • (1997) Boll. Un. Mat. Ital. , vol.11 , Issue.7 , pp. 463-483
    • Serra, S.1
  • 34
    • 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
  • 35
    • 0041110694 scopus 로고    scopus 로고
    • New PCG based methods for Hermitian Toeplitz systems
    • in press
    • S. Serra, New PCG based methods for Hermitian Toeplitz systems, Calcolo, in press.
    • Calcolo
    • Serra, S.1
  • 38
    • 0041110697 scopus 로고    scopus 로고
    • On the asymptotic distribution of the eigenvalues of Hermitian Toeplitz matrices with Toeplitz blocks
    • in press
    • P. Tilli, On the asymptotic distribution of the eigenvalues of Hermitian Toeplitz matrices with Toeplitz blocks, Math. Comp., in press.
    • Math. Comp.
    • Tilli, P.1
  • 39
    • 0011618378 scopus 로고    scopus 로고
    • Singular values and eigenvalues of non-Hermitian block Toeplitz matrices
    • in press
    • P. Tilli, Singular values and eigenvalues of non-Hermitian block Toeplitz matrices, Linear Algebra Appl., in press.
    • Linear Algebra Appl.
    • Tilli, P.1
  • 41
    • 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. 232:1-43 (1996).
    • (1996) Linear Algebra Appl. , vol.232 , pp. 1-43
    • Tyrtyshnikov, E.1
  • 42
    • 0001587020 scopus 로고
    • Szegö limit theorem: The higher dimensional matrix case
    • H. Widom, Szegö limit theorem: The higher dimensional matrix case, J. Funct. Anal. 39:182-198 (1980).
    • (1980) J. Funct. Anal. , vol.39 , pp. 182-198
    • Widom, H.1
  • 43
    • 84968509710 scopus 로고
    • On the eigenvalues of certain Hermitian operators
    • H. Widom, On the eigenvalues of certain Hermitian operators, Trans. Amer. Math. Soc. 88:491-522 (1958).
    • (1958) Trans. Amer. Math. Soc. , vol.88 , pp. 491-522
    • Widom, H.1
  • 44
    • 0000761009 scopus 로고
    • On the singular values of Toeplitz matrices
    • H. Widom, On the singular values of Toeplitz matrices, Z. Anal. Anwendungen 8:221-229 (1989).
    • (1989) Z. Anal. Anwendungen , vol.8 , pp. 221-229
    • Widom, H.1
  • 45
    • 0000807580 scopus 로고
    • Toeplitz matrices
    • (I. Hirshman, Jr., Ed.), Math. Assoc. Amer.
    • H. Widom, Toeplitz matrices, in Studies in Real and Complex Analysis (I. Hirshman, Jr., Ed.), Math. Assoc. Amer., 1965.
    • (1965) Studies in Real and Complex Analysis
    • Widom, H.1


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