The Floquet exponents of the matrix-valued version of the finite Hill equation can be calculated as the zeros of an infinite determinant. In this paper the convergence of this determinant is improved by splitting up suitable infinite products where the definition of such products is based on the knowledge of the asymptotic behaviour of the finite section determinants. For both, the symmetric and the non-symmetric case of the finite Hill equation several methods of convergence acceleration are presented. Numerical examples show that these methods lead to an efficient evaluation of the infinite determinant. [References: 16]
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