Summary
The characteristic exponent ν of the finite Hill differential equation
can be evaluated from the relations
or
whereS (μ) andC (μ) are certain infinite band matrices. According to Mennicken [3] the convergence of the infinite determinants can be accelerated by splitting up suitable infinite products. In the present paper this method is discussed under numerical aspects, moreover the formulas for the infinite products are simplified in such way that the complex Gamma-function is no longer needed. Finally, the presented determinental method is compared with other methods by means of some numerical examples.
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Wagenführer, E. Die Determinantenmethode zur Berechnung des charakteristischen Exponenten der endlichen Hillschen Differentialgleichung. Numer. Math. 35, 405–420 (1980). https://doi.org/10.1007/BF01399008
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DOI: https://doi.org/10.1007/BF01399008