CALCOLO

, Volume 30, Issue 2, pp 171–187 | Cite as

Stima dell'errore nel calcolo degli autovettori nel problema del “buckling” di una piastra incastrata al bordo

  • A. Aimi
  • M. Diligenti
Article

Abstract

Exploiting recent results for the approximation of eigenvectors of a positive compact operator, we present formulas for error estimation in the approximation of eigenvectors of the classical buckling eigenvalue problem for a square plate clamped along its boundary. Tables containing estimates of the error in the Rayleigh-Ritz approximation of the first eigenvectors of the problem are given and the functions approximating first eigenvectors are expressed explicitely. The graphics of these functions show previously studied symmetries.

Keywords

Eigenvalue Problem Allo Studio Algebraic Eigenvalue Problem Intermediate Problem Positive Compact Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliografia

  1. [1]
    A. Aimi, M. Diligenti,Difetti ed eccessi degli autovalori del classico problema di «Buckling», Calcolo (3–4),29 (1992), 313–328.MATHMathSciNetGoogle Scholar
  2. [2]
    L. Bassotti,Su un problema di autovalori per l'elasticità piana, Riv. Mat. Univ. Parma (2),8 (1967), 259–289.MATHMathSciNetGoogle Scholar
  3. [3]
    G. Fichera,Approximation of the eigenvectors of a positive compact operator and estimate of the error, Ann. Mat. Pura App. IV, CVIII, (1976), 367–377.CrossRefMathSciNetGoogle Scholar
  4. [4]
    G. Fichera, Lezioni sulla Teoria Spettrale degli Operatori, (1968), Istituto Matematico «G. Castelnuovo», Roma.Google Scholar
  5. [5]
    G. Fichera,Abstract and Numerical Aspects of eigenvalue Theory, Università di Alberta (U.S.A.), (1973), Edmonton.Google Scholar
  6. [6]
    G. Fichera, Linear Elliptic Differential System and Eigenvalue Problems, Lecture Notes in Math.,8, Springer-Verlag, (1965), Berlin.Google Scholar
  7. [7]
    G. H. Golub, C. F. Van Loan, Matrix Computations, (1983), North Oxford Accademic, Oxford.MATHGoogle Scholar
  8. [8]
    C. Moler, L. E. Payne,Bounds for Eigenvalues and Eigenvectors of Symmetric Operators, SIAM J. Numer. Anal.,5, (1968), pp. 64–70.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    P. M. Prenter, Splines and Variational Methods, (1975), John Wiley & Sons, New York.MATHGoogle Scholar
  10. [10]
    A. Weinstein, W. Stenger, Methods of Intermediate Problems for Eigenvalues, (1972), Acad. Press, New-York and London.MATHGoogle Scholar
  11. [11]
    H. G. Wieberger,Error bounds in the Rayleigh-Ritz approximation of Eigenvectors, Journal of Research of the National Bureau of Standards-B. Mathematics and Mathematical Phisics, Vol. n. 4,64B. (1960), 217–225.Google Scholar
  12. [12]
    J. H. Wilkinson, The Algebraic Eigenvalue Problem, (1965), Claredon Univ. Press, Oxford.MATHGoogle Scholar

Copyright information

© Instituto di Elaborazione della Informazione del CNR 1993

Authors and Affiliations

  • A. Aimi
    • 1
  • M. Diligenti
    • 1
  1. 1.Dipartimento di Meccanica, Facoltà di IngegneriaUniversità degli Studi di BresciaBrescia

Personalised recommendations