What is the effect of computing xy on the size of existing relative errors in the stored values of x and y?
This is what I have done:
We have x̃=(1+ε_x)x and ỹ=(1+ε_y)y so that
x̃ỹ =(1 + ε_x + ε_y + ε_x*ε_y) xy
=> (x̃ỹ/xy) - 1 = ε_x + ε_y + ε_x*ε_y
=> ε_xy = ε_x + ε_y + ε_x*ε_y
Do I now get rid of ε_x*ε_y because that error is too small to include? (Is this the correct reason or is it something else?)
So that I'm left with
ε_xy = ε_x + ε_y? If this is correct, what does it mean?