New in Wolfram Mathematica 6: New Generation Numerical Integration ◄ previous | next ►
Choose between State-of-the-Art Methods
In addition to its automatic algorithm selection, Mathematica 6 provides detailed control over methods used. This shows successive points sampled in four different methods.
In[1]:=

Click for copyable input
GraphicsGrid[

 Partition[

  Graphics3D[{Opacity[.5], 

      Line[Block[{t = 0}, 

        Reap[Quiet@

           NIntegrate[Sqrt[x] + Sqrt[y], {x, 0, 1}, {y, 0, 1 - x^2}, 

            EvaluationMonitor :> Sow[{x, y, t++}], Method -> #]][[2, 

         1]]]]}, BoxRatios -> 1] & /@ {Automatic, "LocalAdaptive", 

    "QuasiMonteCarlo", "AdaptiveQuasiMonteCarlo"}, 2]]
Out[1]=