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A generalization of a theorem of Mammana

Roberto Camporesi, Antonio J. Di Scala (2011)

Colloquium Mathematicae

We prove that any linear ordinary differential operator with complex-valued coefficients continuous in an interval I can be factored into a product of first-order operators globally defined on I. This generalizes a theorem of Mammana for the case of real-valued coefficients.

A method for determining constants in the linear combination of exponentials

Jiří Cerha (1996)

Mathematica Bohemica

Shifting a numerically given function b 1 exp a 1 t + + b n exp a n t we obtain a fundamental matrix of the linear differential system y ˙ = A y with a constant matrix A . Using the fundamental matrix we calculate A , calculating the eigenvalues of A we obtain a 1 , , a n and using the least square method we determine b 1 , , b n .

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