Error Propagation Study the error propagation in the computa

Error Propagation. Study the error propagation in the computation 2 ry, as we did in class for 2 z y. Find the expression for the absolute error and the relative error in the answer fl (z)

Solution

delta=&

fl(x)=X(1+&x), fl(y)=Y(1+&y)

fl(z)=fl(fl(x)*fl(y))

      = [X(1+&x)*Y(1+&y)](1+&z)

      =[(X+X&x)*(Y+Y&y)](1+&z)

      =[XY+XY&y+XY&x+XY&x&y](1+&x)

      =XY+XY&y+XY&x+XY&x&y+XY&z+XY&y&z+XY&x&z+XY&x&y&z

      =XY+XY&x+XY&y+XY&z

&z is the roun off error in making the floating point representation for z.

absolute error = fl(z)-xy = XY&x+XY&y+XY&z