Geodesic
Cauchy operator of a non-stationary linear differential equation with a small parameter at the derivative
Sbornik. Mathematics, Tome 196 (2005) no. 8, pp. 1165-1208 Cet article a éte moissonné depuis la source Math-Net.Ru

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A diagonalization algorithm for a matrix pencil depending on a variable and a parameter in the cases when the limiting matrix has a simple spectrum or a multiple eigenvalue for all values of the variable is put forward. The algorithm uses an exhaustive superposition of special similarity transformations. Formulae for the Cauchy operator of a linear non-stationary equation with a small parameter at the derivative and with a matrix pencil are obtained for various degeneracy orders of the structure matrix. 
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K. I. Chernyshov. Cauchy operator of a non-stationary linear differential equation with a small parameter at the derivative. Sbornik. Mathematics, Tome 196 (2005) no. 8, pp. 1165-1208. http://geodesic.mathdoc.fr/item/SM_2005_196_8_a3/

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