A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
The known formula [ ] ( ) 1 1 / Tr N N λ = A , where A is an n n × Hermitian matrix, 1 λ is its dominant eigenvalue and N is a sufficiently large positive integer, is given the modification ( ) 1 1 / Tr N N λ = A . This modification is conjectured to apply to any n n × matrices, whether Hermitian or...
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| Format: | text |
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Animo Repository
2007
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/9832 |
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| Institution: | De La Salle University |
| Summary: | The known formula [ ] ( ) 1 1 / Tr N N λ = A , where A is an n n × Hermitian matrix, 1 λ is its dominant eigenvalue and N is a sufficiently large positive integer, is given the modification ( ) 1 1 / Tr N N λ = A . This modification is conjectured to apply to any n n × matrices, whether Hermitian or not and is converted into an algorithm for obtaining the modulus of the dominant eigenvalue of A . A heuristic basis for the correctness of the latter formula is given. Several numerical examples with graphical representations of their convergences are given, including an unusual case where ongoing steps give alternately the exact value and the successive approximations of the dominant eigenvalue. |
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