Eigensolutions for matrices of special structures

Communications in Numerical Methods in Engineering

Volumn 19, Issue 2, 2003, Pages 125-136

  Kaveh, A ^a   Sayarinejad, M A ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Decomposition; Eigenvalues; Eigenvectors; Graphs; Laplacian; Matrices; Symmetry

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

LAPLACIAN MATRICES;

MATRIX ALGEBRA;

EIGENVALUE;

EID: 0037294717     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.576     Document Type: Article

References (14)

1. Bathe KJ, Wilson EL. Numerical Methods for Finite Element Analysis. Prentice Hall: Englewood Cliffs, NJ, 1976.
2. Jennings A, McKeown JJ. Matrix Computation. Wiley: New York, 1992.
3. Livesley RK. Mathematical Methods for Engineers. Ellis Horwood: Chichester, U.K., 1989,
4. Biggs NL. Algebraic Graph Theory (2nd edn). Cambridge University Press: Cambridge, 1993.
5. Chung JJ. Spectral Graph Theory. CBMS, Number 92. American Mathematical Society: Providence, RI, 1997.
6. Mohar B. The Laplacian spectrum of graphs. In Graph Theory, Combinatorics and Applications, vol. 2, Alavi Y, Chartrand G, Ollermann OR, Schwenk AJ (eds), Wiley: New York, 1991; 871-898.
7. Paulino GH, Menezes IFM, Gattas M, Mukherjee S. Node and element resequencing using Laplacian of finite element graph: Pan I-general concepts and algorithms. International Journal for Numerical Methods in Engineering 1994; 37:1511-1530.
8. Kaveh A, Rahimi Bondarabady HA. Ordering for wavefront optimization. Computers and Structures 2000; 78:227-235.
9. Kaveh A, Rahimi Bondarabady HA. Finite element mesh decompositions using complementary Laplacian matrix. Communications in Numerical Methods in Engineering 2000; 16:379-389.
10. Kaveh A. Optimal Structural Analysis. Research Studies Press (Wiley): U.K., 1997.
11. Kuo SS. Computer Applications of Numerical Methods. Addison-Wesley: Reading, MA, 1972.
12. Given W. A method of computing eigenvalues and eigenvectors suggested by classical results on symmetric matrices. National Bureau of Standards Applied Mathematics Series 1953; 29:117-122,
13. Ebertein PJ. A Jacobi-like method for the automatic computation of eigenvalues and eigenvectors of an arbitrary matrix. Journal of the Society for Industrial and Applied Mathematics 1962; 10:74-88.
14. Matlab. A program developed by Matworks Inc., Version 4.2, User Guide 1984-1994. www.mathworks.com