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Volumn 45, Issue 2, 2007, Pages 746-769

On the asymptotic spectrum of finite element matrix sequences

Author keywords

Asymptotic eigenvalue distribution; Finite element methods; Matrix sequence

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 36049011181     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/05063533X     Document Type: Article
Times cited : (50)

References (41)
  • 1
    • 42649104903 scopus 로고    scopus 로고
    • T. APEL, Anisotropic Finite Elements: Local Estimates and Applications, Adv. Numer. Math., Teubner, Stuttgart, Germany, 1999.
    • T. APEL, Anisotropic Finite Elements: Local Estimates and Applications, Adv. Numer. Math., Teubner, Stuttgart, Germany, 1999.
  • 3
    • 0000696639 scopus 로고
    • On the rate of convergence of the preconditioned conjugate gradient method
    • O. AXELSSON AND G. LINDSKOG, On the rate of convergence of the preconditioned conjugate gradient method, Numer. Math., 48 (1986), pp. 499-523.
    • (1986) Numer. Math , vol.48 , pp. 499-523
    • AXELSSON, O.1    LINDSKOG, G.2
  • 4
    • 0035733975 scopus 로고    scopus 로고
    • Superlinear convergence of conjugate gradients
    • B. BECKERMANN AND A. B. J. KUIJLAARS, Superlinear convergence of conjugate gradients, SIAM J. Numer. Anal., 39 (2001), pp. 300-329.
    • (2001) SIAM J. Numer. Anal , vol.39 , pp. 300-329
    • BECKERMANN, B.1    KUIJLAARS, A.B.J.2
  • 5
    • 3042580768 scopus 로고    scopus 로고
    • On the sharpness of an asymptotic error estimate for conjugate gradients
    • B. BECKERMANN AND A. B. J. KUIJLAARS, On the sharpness of an asymptotic error estimate for conjugate gradients, BIT, 41 (2001), pp. 856-867.
    • (2001) BIT , vol.41 , pp. 856-867
    • BECKERMANN, B.1    KUIJLAARS, A.B.J.2
  • 6
    • 3042624885 scopus 로고    scopus 로고
    • Superlinear CG convergence for special right-hand sides
    • B. BECKERMANN AND A. B. J. KUIJLAARS, Superlinear CG convergence for special right-hand sides, Electron. Trans. Numer. Anal., 14 (2002), pp. 1-19.
    • (2002) Electron. Trans. Numer. Anal , vol.14 , pp. 1-19
    • BECKERMANN, B.1    KUIJLAARS, A.B.J.2
  • 7
    • 12944291389 scopus 로고    scopus 로고
    • Preconditioned HSS method for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation
    • D. BERTACCINI, G. GOLUB, S. SERRA CAPIZZANO, AND C. TABLINO POSSIO, Preconditioned HSS method for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation, Numer. Math., 99 (2005), pp. 441-484.
    • (2005) Numer. Math , vol.99 , pp. 441-484
    • BERTACCINI, D.1    GOLUB, G.2    SERRA CAPIZZANO, S.3    TABLINO POSSIO, C.4
  • 11
    • 0000161555 scopus 로고
    • On direct methods for solving Poisson's equations
    • B. L. BUZBEE, G. H. GOLUB, AND C. W. NIELSON, On direct methods for solving Poisson's equations, SIAM J. Numer. Anal., 7 (1970), pp. 627-656.
    • (1970) SIAM J. Numer. Anal , vol.7 , pp. 627-656
    • BUZBEE, B.L.1    GOLUB, G.H.2    NIELSON, C.W.3
  • 12
    • 0015202899 scopus 로고
    • The direct solutions of the discrete Poisson equation on irregular regions
    • B. L. BUZBEE, F. W. DORR, J. A. GEORGE, AND G. H. GOLUB, The direct solutions of the discrete Poisson equation on irregular regions, SIAM J. Numer. Anal., 8 (1971), pp. 722-736.
    • (1971) SIAM J. Numer. Anal , vol.8 , pp. 722-736
    • BUZBEE, B.L.1    DORR, F.W.2    GEORGE, J.A.3    GOLUB, G.H.4
  • 14
    • 0014766213 scopus 로고
    • The direct solution of the discrete Poisson equation on a rectangle
    • F. W. DORR, The direct solution of the discrete Poisson equation on a rectangle, SIAM Rev., 12 (1970), pp. 248-263.
    • (1970) SIAM Rev , vol.12 , pp. 248-263
    • DORR, F.W.1
  • 15
    • 0015667999 scopus 로고
    • Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices
    • I. FRIED, Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices, Internat. J. Solids Structures, 9 (1973), pp. 1013-1034.
    • (1973) Internat. J. Solids Structures , vol.9 , pp. 1013-1034
    • FRIED, I.1
  • 16
    • 33751322378 scopus 로고    scopus 로고
    • The asymptotic properties of the spectrum of non symmetrically perturbed Jacobi matrix sequences
    • L. GOLINSKII AND S. SERRA CAPIZZANO, The asymptotic properties of the spectrum of non symmetrically perturbed Jacobi matrix sequences, J. Approx. Theory, 144 (2007), pp. 84-102.
    • (2007) J. Approx. Theory , vol.144 , pp. 84-102
    • GOLINSKII, L.1    SERRA CAPIZZANO, S.2
  • 18
    • 33745213343 scopus 로고    scopus 로고
    • Can one hear the composition of a drum? Mediterranean
    • S. HOLMGREN, S. SERRA CAPIZZANO, AND P. SUNDQVIST, Can one hear the composition of a drum? Mediterranean J. Math., 3 (2006), pp. 227-249.
    • (2006) J. Math , vol.3 , pp. 227-249
    • HOLMGREN, S.1    SERRA CAPIZZANO, S.2    SUNDQVIST, P.3
  • 21
    • 0008515049 scopus 로고    scopus 로고
    • Preconditioning Chebyshev spectral collocation by finite-differences operators
    • S. D. KIM AND S. V. PARTER, Preconditioning Chebyshev spectral collocation by finite-differences operators, SIAM J. Numer. Anal., 34 (1997), pp. 939-958.
    • (1997) SIAM J. Numer. Anal , vol.34 , pp. 939-958
    • KIM, S.D.1    PARTER, S.V.2
  • 22
    • 0035194266 scopus 로고    scopus 로고
    • Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients
    • A. B. J. KUIJLAARS AND S. SERRA CAPIZZANO, Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients, J. Approx. Theory, 113 (2001), pp. 142-155.
    • (2001) J. Approx. Theory , vol.113 , pp. 142-155
    • KUIJLAARS, A.B.J.1    SERRA CAPIZZANO, S.2
  • 23
    • 0006811866 scopus 로고
    • On the eigenvalues of certain generalizations of Toeplitz matrices
    • S. PARTER, On the eigenvalues of certain generalizations of Toeplitz matrices, Arch. Ration. Math. Mech., 3 (1962), pp. 244-257.
    • (1962) Arch. Ration. Math. Mech , vol.3 , pp. 244-257
    • PARTER, S.1
  • 26
    • 0034144763 scopus 로고    scopus 로고
    • Locally X matrices, spectral distributions, preconditioning, and applications
    • S. SERRA CAPIZZANO, Locally X matrices, spectral distributions, preconditioning, and applications, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1354-1388.
    • (2000) SIAM J. Matrix Anal. Appl , vol.21 , pp. 1354-1388
    • SERRA CAPIZZANO, S.1
  • 27
    • 0034174162 scopus 로고    scopus 로고
    • Some theorems on linear positive operators and functionals and their applications
    • S. SERRA CAPIZZANO, Some theorems on linear positive operators and functionals and their applications, Comput. Math. Appl., 39 (2000), pp. 139-167.
    • (2000) Comput. Math. Appl , vol.39 , pp. 139-167
    • SERRA CAPIZZANO, S.1
  • 28
    • 0041754434 scopus 로고    scopus 로고
    • A note on the asymptotic spectra of finite difference discretizations of second order elliptic partial differential equations
    • S. SERRA CAPIZZANO, A note on the asymptotic spectra of finite difference discretizations of second order elliptic partial differential equations, Asian J. Math., 4 (2000), pp. 499-514.
    • (2000) Asian J. Math , vol.4 , pp. 499-514
    • SERRA CAPIZZANO, S.1
  • 29
    • 0035342317 scopus 로고    scopus 로고
    • Distribution results on the algebra generated by Toeplitz sequences: A finite dimensional approach
    • S. SERRA CAPIZZANO, Distribution results on the algebra generated by Toeplitz sequences: A finite dimensional approach, Linear Algebra Appl., 328 (2001), pp. 121-130.
    • (2001) Linear Algebra Appl , vol.328 , pp. 121-130
    • SERRA CAPIZZANO, S.1
  • 30
    • 0035501546 scopus 로고    scopus 로고
    • Spectral behaviour of matrix sequences and discretized boundary value problems
    • S. SERRA CAPIZZANO, Spectral behaviour of matrix sequences and discretized boundary value problems, Linear Algebra Appl., 337 (2001), pp. 37-78.
    • (2001) Linear Algebra Appl , vol.337 , pp. 37-78
    • SERRA CAPIZZANO, S.1
  • 31
    • 0037409955 scopus 로고    scopus 로고
    • Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
    • S. SERRA CAPIZZANO, Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations, Linear Algebra Appl., 366 (2003), pp. 371-402.
    • (2003) Linear Algebra Appl , vol.366 , pp. 371-402
    • SERRA CAPIZZANO, S.1
  • 32
    • 33748294500 scopus 로고    scopus 로고
    • GLT sequences as a generalized Fourier analysis and applications
    • S. SERRA CAPIZZANO, GLT sequences as a generalized Fourier analysis and applications, Linear Algebra Appl., 419 (2006), pp. 180-233.
    • (2006) Linear Algebra Appl , vol.419 , pp. 180-233
    • SERRA CAPIZZANO, S.1
  • 33
    • 0008465849 scopus 로고    scopus 로고
    • Spectral and structural analysis of high precision finite difference matrices for elliptic operators
    • S. SERRA CAPIZZANO AND C. TABLINO 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    TABLINO POSSIO, C.2
  • 34
    • 0035565674 scopus 로고    scopus 로고
    • Finite element matrix-sequences: The case of rectangular domains
    • S. SERRA CAPIZZANO AND C. TABLINO POSSIO, Finite element matrix-sequences: The case of rectangular domains, Numer. Algorithms, 28 (2001), pp. 309-327.
    • (2001) Numer. Algorithms , vol.28 , pp. 309-327
    • SERRA CAPIZZANO, S.1    TABLINO POSSIO, C.2
  • 35
    • 0038382932 scopus 로고    scopus 로고
    • Analysis of preconditioning strategies for collocation linear systems
    • S. SERRA CAPIZZANO AND C TABLINO POSSIO, Analysis of preconditioning strategies for collocation linear systems, Linear Algebra Appl., 369 (2003), pp. 41-75.
    • (2003) Linear Algebra Appl , vol.369 , pp. 41-75
    • SERRA CAPIZZANO, S.1    TABLINO POSSIO, C.2
  • 36
    • 1342310012 scopus 로고    scopus 로고
    • Superlinear preconditioned for finite differences linear systems
    • S. SERRA CAPIZZANO AND C TABLINO POSSIO, Superlinear preconditioned for finite differences linear systems, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 152-164.
    • (2003) SIAM J. Matrix Anal. Appl , vol.25 , pp. 152-164
    • SERRA CAPIZZANO, S.1    TABLINO POSSIO, C.2
  • 38
    • 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
  • 39
    • 3042570112 scopus 로고    scopus 로고
    • A uniform approach to some old and new theorems on distribution and clustering
    • E. E. TYRTYSHNIKOV, A uniform approach to some old and new theorems on distribution and clustering, Linear Algebra Appl., 232 (1996), pp. 1-43.
    • (1996) Linear Algebra Appl , vol.232 , pp. 1-43
    • TYRTYSHNIKOV, E.E.1
  • 40
    • 0006770755 scopus 로고    scopus 로고
    • A matrix view on the root distribution for orthogonal polynomials
    • D. Bini, E. Tyrtyshnikov, and P. Yalamov, eds, Nova Science, New York
    • E. E. TYRTYSHNIKOV, A matrix view on the root distribution for orthogonal polynomials, in Structured Matrices: Recent Developments in Theory and Computation, D. Bini, E. Tyrtyshnikov, and P. Yalamov, eds., Nova Science, New York, 2001, pp. 149-156.
    • (2001) Structured Matrices: Recent Developments in Theory and Computation , pp. 149-156
    • TYRTYSHNIKOV, E.E.1
  • 41
    • 0001403122 scopus 로고
    • The rate of convergence of conjugate gradients
    • A. VAN DER SLUIS AND H. A. VAN DER VORST, The rate of convergence of conjugate gradients, Numer. Math., 48 (1986), pp. 543-560.
    • (1986) Numer. Math , vol.48 , pp. 543-560
    • VAN, A.1    SLUIS, D.2    VAN DER VORST, H.A.3


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