Linear transformation from [-1,1] to [a,b]

[mercuryman]

Hey
This is from Numerical analysis course (Legendre polynom) - they gave us the polynomial transformation from [-1,1] to [a,b] as: x = 2/(b-a) * z - (b+a)/(b-a)
what is the proof of this tranformation? where did it come from?
thanks

 

[pasmith]

Hey
This is from Numerical analysis course (Legendre polynom) - they gave us the polynomial transformation from [-1,1] to [a,b] as: x = 2/(b-a) * z - (b+a)/(b-a)
what is the proof of this tranformation? where did it come from?
thanks

That isn't the transformation from [-1,1] to [a,b]; it's the transformation from [a,b] to [-1,1].

As for where it comes from: set x = mz + c, and impose the conditions that x = -1 when z = a and x = 1 when z = b. That gives you two linear simultaneous equations for m and c:
$$-1 = ma + c \\ 1 = mb + c$$