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

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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
 

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pasmith
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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:
[tex]
-1 = ma + c \\
1 = mb + c
[/tex]
 

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