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The stability of the Nystr\"om method for the double layer potential equationon simple closed piecewise smooth contours is studied. Necessary and sufficientconditions of the stability of the method are established. It is shown that themethod under consideration is stable if and only if certain operatorsassociated with the opening angles of the corner points are invertible.Numerical experiments show that there are opening angles which causeinstability of the method.

The stability of the Nystr\"om method for double layer potential equations