ii Formulate the theorem describing the properties of the mi

ii) Formulate the theorem describing the properties of the minimax error. Apply the theorem to this approximation.

Solution

define error function E(x) = 1/(1+x) - ax-b

where a and b are constants which defines the linear function

error is supposed to be ma at end points.

E(0) = 1/(1+0)-b = 1-b

E(1) = 1/(1+1) -a-b = 0.5 - a - b

error is max at 0 and 1 so

1-b = 0.5 - a-b

a= -0.5

b can be any value