Geodesic
Constructive Solvability Conditions for the Riemann--Hilbert Problem
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 643-655.

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Sufficient and necessary conditions for the solvability of the Riemann–Hilbert problem are studied. These conditions consist in the possibility of constructing stable and semistable pairs (of bundles and connections) for a given monodromy. The obtained results make it possible to develop algorithms for testing the solvability conditions for the Riemann–Hilbert problem. 
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     title = {Constructive {Solvability} {Conditions} for the {Riemann--Hilbert} {Problem}},
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I. V. Vyugin. Constructive Solvability Conditions for the Riemann--Hilbert Problem. Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 643-655. http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a0/

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