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- W2024336882 abstract "Using distinct non zero diagonal elements of a Hermitian (or anti Hermitian) matrix as independent variables of the characteristicpolynomial function, a Newton's algorithm is developed for the solution of the inverse eigenproblem given distinct nonzero eigenvalues. It is found that if a 2$times$2 singular Hermitian (or singular anti Hermitian) matrix of rank one is used as the initial matrix, convergence to an exact solution is achieved in only one step. This result can be extended to $n times n$ matrices provided the target eigenvalues are respectively of multiplicities $p$ and $q$ with $p+q=n$ and $ 1 leq p,q < n$. Moreover, the initial matrix would be of rank one and would have only two distinct corresponding nonzero diagonal elements, the rest being repeated. To illustrate the result, numerical examples are given for the cases $n=2, 3$ and $4$." @default.
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- W2024336882 date "2014-04-18" @default.
- W2024336882 modified "2023-09-26" @default.
- W2024336882 title "Solution of the Inverse Eigenvalue Problem for Certain (Anti-) Hermitian Matrices Using Newton's Method" @default.
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- W2024336882 doi "https://doi.org/10.5539/jmr.v6n2p64" @default.
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