A Reduction of the Eigenproblem for Hermitian Toeplitz Matrices.
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Call the problem of finding the eigenvalues and a complete set of linearly independent eigenvectors of an n-th order Hermitian Toeplitz matrix, R, the eigenproblem. In the report, exploring the structure of the eigenspace of a typical eigenvalue of R, the author derives a method to solve the eigenproblem for R by solving the eigenproblem for an n-th order real symmetric matrix by either Jacobis method or the Givens-Householder method and inverse iteration. If R is real symmetric, then its eigenproblem reduces to the eigenproblems for two smaller real symmetric matrices. This simplification of the eigenproblem economizes on the use of main computer memory. Author
- Theoretical Mathematics