A robust algorithm for finding the eigenvalues and eigenvectors of 3 x 3 symmetric matrices

Many concepts in continuum mechanics are most easily understood in principal coordinates; using these concepts in a numerical analysis requires a robust algorithm for finding the eigenvalues and eigenvectors of 3 X 3 symmetric matrices. A robust algorithm for solving this eigenvalue problem is prese...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2008-08, Vol.197 (45-48), p.4007-4015
Main Authors: SCHERZINGER, W. M, DOHRMANN, C. R
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Online Access:Get full text
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Summary:Many concepts in continuum mechanics are most easily understood in principal coordinates; using these concepts in a numerical analysis requires a robust algorithm for finding the eigenvalues and eigenvectors of 3 X 3 symmetric matrices. A robust algorithm for solving this eigenvalue problem is presented along with an analysis of the algorithm. The special case of two or three nearly identical eigenvalues is examined in detail using an asymptotic analysis. Numerical results are shown that compare this algorithm with existing methods found in the literature. The behavior of this algorithm is shown to be more reliable than the other methods with a minimal computational cost.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2008.03.031