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

  1. Sep 18, 2013 #1
    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
     
  2. jcsd
  3. Sep 18, 2013 #2

    pasmith

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    Homework Helper

    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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