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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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- Thread starter mercuryman
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- #1

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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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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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