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Eigensolution of specially structured matrices with hyper‐symmetry
Author(s) -
Kaveh A.,
Sayarinejad M. A.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1660
Subject(s) - generalization , eigenvalues and eigenvectors , symmetry (geometry) , simple (philosophy) , mathematics , stability (learning theory) , algebra over a field , combinatorics , computer science , pure mathematics , mathematical analysis , geometry , physics , philosophy , epistemology , quantum mechanics , machine learning
Recently, four canonical forms have been developed and applied to the dynamics and stability analysis of symmetric frames. In this paper, hyper‐symmetric matrices and specially structured matrices are defined and efficient methods are proposed for the eigensolution of such matrices. Applications are extended to hyper‐graphs and specially structured graphs. Simple methods are developed for calculating the eigenvalues of the Laplacian matrices of such graphs. The developments presented in this paper can also be considered as generalization of Form II and Form III symmetry, previously defined by the authors. Copyright © 2006 John Wiley & Sons, Ltd.