메뉴 건너뛰기




Volumn 45, Issue 6, 2007, Pages 2345-2367

Spectral analysis of nonsymmetric quasi-toeplitz matrices with applications to preconditioned multistep formulas

Author keywords

Boundary value problems; Circulant preconditioners; Difference equations; Eigenvalues; Linear multistep formulas; Linear systems of time step integrators; Nonsymmetric Toeplitz matrices

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTION EVALUATION; INITIAL VALUE PROBLEMS; LINEAR EQUATIONS; LINEAR SYSTEMS; SPECTRUM ANALYSIS; SPECTRUM ANALYZERS;

EID: 55549121945     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/060650349     Document Type: Article
Times cited : (6)

References (34)
  • 1
    • 84966215337 scopus 로고
    • Boundary value techniques for initial value problems in ordinary differential equations
    • A. O. H. AXELSSON AND J. G. VERWER, Boundary value techniques for initial value problems in ordinary differential equations, Math. Comp., 45 (1985), pp. 153-171.
    • (1985) Math. Comp , vol.45 , pp. 153-171
    • AXELSSON, A.O.H.1    VERWER, J.G.2
  • 2
    • 0000851041 scopus 로고
    • The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices
    • R. M. BEAM AND R. F. WARMING, The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices, SIAM J. Sci. Comput., 14 (1993), pp. 971-1006.
    • (1993) SIAM J. Sci. Comput , vol.14 , pp. 971-1006
    • BEAM, R.M.1    WARMING, R.F.2
  • 3
    • 0004764563 scopus 로고    scopus 로고
    • P-circulant preconditioners and the systems of ODE codes
    • Iterative Methods in Scientific Computation IV, D. R. Kincaid et al, eds, IMACS, NJ
    • D. BERTACCINI, P-circulant preconditioners and the systems of ODE codes, in Iterative Methods in Scientific Computation IV, IMACS Series in Computational and Applied Mathematics, D. R. Kincaid et al., eds., IMACS, NJ, 1999, pp. 179-193.
    • (1999) IMACS Series in Computational and Applied Mathematics , pp. 179-193
    • BERTACCINI, D.1
  • 4
    • 0034975734 scopus 로고    scopus 로고
    • A circulant preconditioner for the systems of LMF-based ODE codes
    • D. BERTACCINI, A circulant preconditioner for the systems of LMF-based ODE codes, SIAM J. Sci. Comput., 22 (2000), pp. 767-786.
    • (2000) SIAM J. Sci. Comput , vol.22 , pp. 767-786
    • BERTACCINI, D.1
  • 5
    • 0035578458 scopus 로고    scopus 로고
    • Reliable preconditioned iterative linear solvers for some numerical integrators
    • D. BERTACCINI, Reliable preconditioned iterative linear solvers for some numerical integrators, Numer. Linear Algebra Appl., 8 (2001), pp. 111-125.
    • (2001) Numer. Linear Algebra Appl , vol.8 , pp. 111-125
    • BERTACCINI, D.1
  • 6
    • 0043142566 scopus 로고    scopus 로고
    • The convergence rate of block preconditioned systems arising from LMF-based ODE codes
    • D. BERTACCINI AND M. K. NG, The convergence rate of block preconditioned systems arising from LMF-based ODE codes, BIT, 41 (2001), pp. 433-450.
    • (2001) BIT , vol.41 , pp. 433-450
    • BERTACCINI, D.1    NG, M.K.2
  • 7
    • 0042602255 scopus 로고    scopus 로고
    • The spectrum of circulant-like preconditioners for some general linear multistep formulas for linear boundary value problems
    • D. BERTACCINI, The spectrum of circulant-like preconditioners for some general linear multistep formulas for linear boundary value problems, SIAM J. Numer. Anal., 40 (2002), pp. 1798-1822.
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 1798-1822
    • BERTACCINI, D.1
  • 8
    • 0042914754 scopus 로고    scopus 로고
    • Block {ω}-circulant preconditioners for the systems of differential equations
    • D. BERTACCINI AND M. K. NG, Block {ω}-circulant preconditioners for the systems of differential equations, Calcolo, 40 (2003), pp. 71-90.
    • (2003) Calcolo , vol.40 , pp. 71-90
    • BERTACCINI, D.1    NG, M.K.2
  • 9
    • 4043123210 scopus 로고    scopus 로고
    • Band-Toeplitz preconditioned GMRES iterations for time-dependent PDEs
    • D. BERTACCINI AND M. K. NG, Band-Toeplitz preconditioned GMRES iterations for time-dependent PDEs, BIT, 43 (2003), pp. 901-914.
    • (2003) BIT , vol.43 , pp. 901-914
    • BERTACCINI, D.1    NG, M.K.2
  • 10
    • 20744441827 scopus 로고    scopus 로고
    • The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form
    • D. BERTACCINI, Y. WEN, AND M. K. NG, The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form, Numer. Linear Algebra Appl., 12 (2005), pp. 315-325.
    • (2005) Numer. Linear Algebra Appl , vol.12 , pp. 315-325
    • BERTACCINI, D.1    WEN, Y.2    NG, M.K.3
  • 11
    • 0034396488 scopus 로고    scopus 로고
    • Design, analysis and implementation of a multiprecision polynomial rootfinder
    • D. BINI AND G. FIORENTINO, Design, analysis and implementation of a multiprecision polynomial rootfinder, Numer. Algorithms, 23 (2000), pp. 127-173.
    • (2000) Numer. Algorithms , vol.23 , pp. 127-173
    • BINI, D.1    FIORENTINO, G.2
  • 15
    • 0002636630 scopus 로고
    • Circulant preconditioners for elliptic problems
    • R. H. CHAN AND T. CHAN, Circulant preconditioners for elliptic problems, Numer. Linear Algebra Appl., 1 (1992), pp. 77-101.
    • (1992) Numer. Linear Algebra Appl , vol.1 , pp. 77-101
    • CHAN, R.H.1    CHAN, T.2
  • 16
    • 0030246195 scopus 로고    scopus 로고
    • Conjugate gradient methods for Toeplitz systems
    • R. H. CHAN AND M. K. NG, Conjugate gradient methods for Toeplitz systems, SIAM Rev., 38 (1996), pp. 427-482.
    • (1996) SIAM Rev , vol.38 , pp. 427-482
    • CHAN, R.H.1    NG, M.K.2
  • 17
    • 55549138851 scopus 로고    scopus 로고
    • Circulant preconditioners for solving ordinary differential equations, in Structured Matrices
    • Bini D. et al. eds, NY
    • R. H. CHAN, M. K. NG, AND X. Q. JIN, Circulant preconditioners for solving ordinary differential equations, in Structured Matrices, Bini D. et al. eds., Nova Science, Hauppauge, NY, 2001.
    • (2001) Nova Science, Hauppauge
    • CHAN, R.H.1    NG, M.K.2    JIN, X.Q.3
  • 18
    • 0000853646 scopus 로고
    • An optimal circulant preconditioner for Toeplitz systems
    • T. F. CHAN, An optimal circulant preconditioner for Toeplitz systems, SIAM J. Sci. Comput., 9 (1988), pp. 766-771.
    • (1988) SIAM J. Sci. Comput , vol.9 , pp. 766-771
    • CHAN, T.F.1
  • 20
    • 34547351968 scopus 로고
    • A note on the numerical integration of first-order differential equations
    • L. FOX, A note on the numerical integration of first-order differential equations, Quart. J. Mech. Appl. Math., 7 (1954), pp. 367-378.
    • (1954) Quart. J. Mech. Appl. Math , vol.7 , pp. 367-378
    • FOX, L.1
  • 25
    • 0001580455 scopus 로고    scopus 로고
    • Analysis of preconditioners for hyperbolic partial differential equations
    • K. OTTO, Analysis of preconditioners for hyperbolic partial differential equations, SIAM J. Numer. Anal., 33 (1996), pp. 2131-2165.
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 2131-2165
    • OTTO, K.1
  • 26
    • 0000648360 scopus 로고
    • Time-independent scattering theory for time-periodic Hamiltonians: Formulation and complex scaling calculations of above threshold ionization spectra
    • U. PESKIN AND N. MOISEYEV, Time-independent scattering theory for time-periodic Hamiltonians: Formulation and complex scaling calculations of above threshold ionization spectra, Phys. Rev. A, 49 (1994), pp. 3712-3728.
    • (1994) Phys. Rev. A , vol.49 , pp. 3712-3728
    • PESKIN, U.1    MOISEYEV, N.2
  • 27
    • 0033480798 scopus 로고    scopus 로고
    • The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems
    • S. SERRA, The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems, Numer. Math., 81 (1999), pp. 461-495.
    • (1999) Numer. Math , vol.81 , pp. 461-495
    • SERRA, S.1
  • 28
    • 0008465849 scopus 로고    scopus 로고
    • Spectral and structural analysis of high precision finite difference matrices for elliptic operators
    • S. SERRA-CAPIZZANO AND C. T. POSSIO, Spectral and structural analysis of high precision finite difference matrices for elliptic operators, Linear Algebra Appl., 293 (1999), pp. 85-131.
    • (1999) Linear Algebra Appl , vol.293 , pp. 85-131
    • SERRA-CAPIZZANO, S.1    POSSIO, C.T.2
  • 29
    • 0022694911 scopus 로고
    • A proposal for Toeplitz matrix calculations
    • G. STRANG, A proposal for Toeplitz matrix calculations, Stud. Appl. Math., 74 (1986), pp. 171-176.
    • (1986) Stud. Appl. Math , vol.74 , pp. 171-176
    • STRANG, G.1
  • 31
    • 11544297717 scopus 로고    scopus 로고
    • Locally Toeplitz sequences: Spectral properties and applications
    • P. TILLI, Locally Toeplitz sequences: Spectral properties and applications, Linear Algebra Appl., 278 (1998), pp. 91-120.
    • (1998) Linear Algebra Appl , vol.278 , pp. 91-120
    • TILLI, P.1
  • 32
    • 0344386943 scopus 로고    scopus 로고
    • Some results on complex Toeplitz eigenvalues
    • P. TILLI, Some results on complex Toeplitz eigenvalues, J. Math. Anal. Appl., 239 (1999), pp. 390-401.
    • (1999) J. Math. Anal. Appl , vol.239 , pp. 390-401
    • TILLI, P.1
  • 33
    • 0000733803 scopus 로고
    • On the eigenvalue problem for Toeplitz band matrices
    • W. F. TRENCH, On the eigenvalue problem for Toeplitz band matrices, Linear Algebra Appl., 64 (1985), pp. 199-214.
    • (1985) Linear Algebra Appl , vol.64 , pp. 199-214
    • TRENCH, W.F.1
  • 34
    • 0000523384 scopus 로고
    • Numerical solution of the eigenvalue problem for Hermitian Toeplitz matrices
    • W. F. TRENCH, Numerical solution of the eigenvalue problem for Hermitian Toeplitz matrices, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 135-146.
    • (1989) SIAM J. Matrix Anal. Appl , vol.10 , pp. 135-146
    • TRENCH, W.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.