Back to Search
Start Over
Shifted Inverse Power Method for Computing the Smallest M-Eigenvalue of a Fourth-Order Partially Symmetric Tensor.
- Source :
-
Journal of Optimization Theory & Applications . Mar2024, Vol. 200 Issue 3, p1131-1159. 29p. - Publication Year :
- 2024
-
Abstract
- The strong ellipticity condition (abbr. SE-condition) of the displacement equations of equilibrium for general nonlinearly elastic materials plays an important role in nonlinear elasticity and materials. Qi et al. (Front Math China 4(2):349–364, 2009) pointed out that the SE-condition of the displacement equations of equilibrium can be equivalently transformed into the SE-condition of a fourth-order real partially symmetric tensor A , and that the SE-condition of A holds if and only if the smallest M-eigenvalue of A is positive. In order to judge the strong ellipticity of A , we propose a shifted inverse power method for computing the smallest M-eigenvalue of A and give its convergence analysis. And then, we borrow and fine-tune an existing initialization strategy to make the sequence generated by the shifted inverse power method rapidly converge to a good approximation of the smallest M-eigenvalue of A . Finally, we by numerical examples illustrate the effectiveness of the proposed method in computing the smallest M-eigenvalue of A and judging the SE-condition of the displacement equations of equilibrium. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EQUILIBRIUM
*ELASTICITY
Subjects
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 200
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 175829397
- Full Text :
- https://doi.org/10.1007/s10957-023-02369-z