Abstract
Eigenvalues and eigenvectors have many applications in structural mechanics and combinatorial optimization. In this paper, a set of matrices of special forms is studied for which the calculation of eigenvalues can be performed much easier than with the existing general methods. First tri-diagonal matrices are presented and then the relationships for calculating their eigenvalues are extended to the evaluation of the eigenvalues of block tri-diagonal matrices. Block penta-diagonal matrices are also studied in this paper. The eigensolution of different problems of structural mechanics is performed to show the simplicity of using the present formulations.
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