Newton Divided Difference Method of Interpolation in maple

Question

Does anyone know how one can do this in maple? find Newton divided difference interpolation polynomial for the function cos2x the points {1, 0.6, 0.3, 0.1, 0}

Answer 1

If this is homework then you could show what you've accomplished on your own already.

If you just need the result then you could try the Student:-NumericalAnalysis package. Eg,

L:=[0, 0.1, 0.3, 0.6, 1]:

p:=Student:-NumericalAnalysis:-PolynomialInterpolation(
               [seq([x,cos(2*x)], x in L)],
               method=newton):

Student:-NumericalAnalysis:-DividedDifferenceTable(p);

  [           1.              0              0             0             0]
  [                                                                       ]
  [ 0.9800665778  -0.1993342220              0             0             0]
  [                                                                       ]
  [ 0.8253356149  -0.7736548145   -1.914401975             0             0]
  [                                                                       ]
  [ 0.3623577545   -1.543259535   -1.539209441  0.6253208900             0]
  [                                                                       ]
  [-0.4161468365   -1.946261478  -0.5757170614   1.070547088  0.4452261980]


interpol:=Student:-NumericalAnalysis:-Interpolant(p,independentvar=x);

      interpol := 1. - 0.1993342220 x - 1.914401975 x (x - 0.1)

         + 0.6253208900 x (x - 0.1) (x - 0.3)

         + 0.4452261980 x (x - 0.1) (x - 0.3) (x - 0.6)

plots:-dualaxisplot(plot([cos(2*x),interpol],x=0..1),
                    plot([cos(2*x)-interpol],x=0..1,legend=`abs. error`));

Programming questions on Maple are often better asked on stackoverflow, unless your central question is about the mathematics behind the algorithm.