Does Claudius think that Hamlet is feinging madness?

If Hamlet is indeed simply acting in a manner to make those around him believe he is mad, does the king hold any suspicions of this? Is Hamlet's act so well orchestrated that he has hoodwinked the sly old fox?

From my personal observations, it seems to me that Claudius is taken in by Hamlet's actions, or else he is as good an actor as the prince. In act 2.2 when Polonius tells him that he knows the cause of Hamlet's madness he says, " Oh, speak of that! That I do long to hear.", and refuses to let the issue drop until Polonius has fully explained it. He devotes a scant few lines to the international affairs of his country, dismisses the ambassadors and hurries back to the subject of Hamlet. There is one point though, where he sounds like he is saying that Hamlet is simply acting. In scene 3.1 he says to Polonius, "...Get from him why he puts on this confusion... with turbulent and dangerous lunacy?". It may be a misenterpreted cojecture on my part to say this, but it could be seen as a hint that he does not believe that Hamlet has truly lost his marbles.