Abstract
The paper considers Levinson algorithms for Hermitian and non-Hermitian Toeplitz matrices that for integer matrices remain fraction-free (FF). A recently introduced FF algorithm is extended from Hermitian to non-symmetric Toeplitz matrices. An alternative proof for the integer-preservation property is obtained by linking the elements of the solution vectors to minors of the Toeplitz matrix. These links are also used to prove that the length of integers grows at a very restrained rate, a property that implies that the algorithms are very efficient integer algorithms.
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