Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices

Diem Ho; Françoise Chatelin; Maria Bennani

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1990)

  • Volume: 24, Issue: 1, page 53-65
  • ISSN: 0764-583X

How to cite

top

Ho, Diem, Chatelin, Françoise, and Bennani, Maria. "Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 24.1 (1990): 53-65. <http://eudml.org/doc/193588>.

@article{Ho1990,
author = {Ho, Diem, Chatelin, Françoise, Bennani, Maria},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Chebyshev acceleration; Arnoldi method; Chebyshev iterations; partial nonsymmetric eigenvalue problem; large matrices; Chebyshev ellipse; complex eigenspectrum; numerical example},
language = {eng},
number = {1},
pages = {53-65},
publisher = {Dunod},
title = {Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices},
url = {http://eudml.org/doc/193588},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Ho, Diem
AU - Chatelin, Françoise
AU - Bennani, Maria
TI - Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1990
PB - Dunod
VL - 24
IS - 1
SP - 53
EP - 65
LA - eng
KW - Chebyshev acceleration; Arnoldi method; Chebyshev iterations; partial nonsymmetric eigenvalue problem; large matrices; Chebyshev ellipse; complex eigenspectrum; numerical example
UR - http://eudml.org/doc/193588
ER -

References

top
  1. [1] F. CHATELIN, Valeurs Propres de Matrices, Masson, Paris, 1988. Zbl0691.65018MR934203
  2. [2] M. CLINT and A. JENNINGS, The Evaluation of Eigenvalues and Eigenvectors of Real Symmetric Matrices by Simultaneous Iteration Method, J. Inst. Math. Appl., 8, 111-121, 1971. Zbl0221.65070MR297116
  3. [3] J. CULLUM and R. A. WILLOUGHBY, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1, Theory, Vol. 2, Programs, Birkhauser, Basel, 1985. Zbl0574.65028
  4. [4] J. CULLUM and R. A. WILLOUGHBY, A Practical Procedure for Computing Eigenvalues of large Sparse Nonsymmetric Matrices, in Large Scale Eigenvalue Problems, eds. J. Cullum and R. A. Willoughby, Elsevier Science Publishers B. V. (North-Holland), 1986. Zbl0605.65027MR875435
  5. [5] D. HO, Tchebychev Iteration and Its Optimal Ellipse for Nonsymmetric Matrices, Tech. Rep. F-125, IBM Scientific Center, Paris, 1987. 
  6. [6] A. JENNINGS, Eigenvalue Methods and the Analysis of Structural Vibration, in Sparse Matrices and Their Uses, ed. I. S. Duff, Academic Press, New York, 109-139, 1981. Zbl0457.73072
  7. [7] A. JENNINGS and W. J. STEWART, Simultaneous Iteration for Partial Eigensolution of Real Matrices, J. Math. Inst. Appl., 15, 351-361, 1980. Zbl0307.65042MR408221
  8. [8] T. A. MANTEUFFEL, An Iterative Method for Solving Nonsymmetric Linear Systems with Dynamic Estimation of Parameters, Ph. D. dissertation, Tech. Rep. UIUCDCS-75-758, University of Illinois, Urbana-Champaign, 1975. 
  9. [9] T. A. MANTEUFFEL, The Tchebychev Iteration for Nonsymmetric Linear Systems, Numer. Math., 28, 307-327, 1977. Zbl0361.65024MR474739
  10. [10] T. A. MANTEUFFEL, Adaptive procedure for Estimation of Parameter for the Non-symmetric Tchebychev Iteration, Numer. Math., 31, 183-208, 1978. Zbl0413.65032MR509674
  11. [11] B. NOUR-OMID, B. N. PARLETT and R. TAYLOR, Lanczos Versus Subspace Iteration for the Solution of Eigenvalue Problems, Int. J. Num. Meth. Engr., 19, 859-871, 1983. Zbl0521.65024
  12. [12] B. N. PARLETT, D. R. TAYLOR and Z. Z. LIU, The look ahead Lanczos algorithm for large nonsymmetric eigenproblems, in Computing methods in applied sciences and engineering, eds. R. Glowinski and J. L. Lions, North Holland, 1985. Zbl0564.65021MR806772
  13. [13] Y. SAAD, Variations on Arnoldi's Method for Computing Eigenelements of Large Unsymmetric Matrices, Linear Algebra Appl., 34, 269-295, 1980. Zbl0456.65017MR591435
  14. [14] Y. SAAD, Least Squares Polynomials in the Complex Plane with Applications to Solving Sparse Nonsymmetric Matrix Problems, Res. Rep. YALEU/DCS/RR-276, 1983. 
  15. [15] Y. SAAD, Tchebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems, Math. Comp., 42, 567-588, 1984. Zbl0539.65013MR736453
  16. [16] Y. SAAD, Partial Eigensolutions of Large Nonsymmetric Matrices, Res. Rep. YALEU/DCS/RR-397, 1985. 
  17. [17] G. W. STEWART, Simultaneous Iteration for Computing Invariant Subspace of non-Hermitian Matrices, Numer. Math., 25, 123-136, 1976. Zbl0328.65025MR400677
  18. [18] D. TAYLOR, Analysis of the Look-Ahead Lanczos Algorithm, Ph. D. Thesis, Tech. Rep., Univ. of California, Berkeley, 1983. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.