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A Recreating chebychev coefficient from an article

  1. Jul 7, 2017 #1
    Hello i need to recreate these chebychev coefficents given the initial value of X_0=1.853 as shown in the photo bellow.
    i have tried to follow the iterrative algorithm shown in the photo bellow.
    please help me understand where did i go wrong?

    thanks

    25fpq2x.jpg

    2qwexbc.jpg
     
  2. jcsd
  3. Jul 7, 2017 #2

    mfb

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    2017 Award

    Staff: Mentor

    What exactly went wrong?
     
  4. Jul 7, 2017 #3
    if x_0=1.853 then
    T_0=1
    T_1=1.853
    T_2=2*1.853*1.853-1
    its not the same numbers that they get in the article

    Thanks
     
  5. Jul 8, 2017 #4

    mfb

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    2017 Award

    Staff: Mentor

    What you calculate are not coefficients of polynomials, these numbers are the values of the polynomial functions at this value of x.

    I don't understand where their numbers come from, but I also don't understand where they are used afterwards. I found the context here, page 19 ("206").

    I also don't understand the value of x they got - WolframAlpha disagrees (using 180 instead of pi doesn't work either, but I guess the 180 comes from working in degrees).
     
  6. Jul 8, 2017 #5
    Hello, Yes this is the article from which the example came from.
    you are correct regarding the wolfram alfa calculation.assuming that their numbers are wrong
    i tried to use matlabs commands for
    g=chebyshevT([1 ,2, 3 ,4] , x) %first kind
    [ x, 2*x^2 - 1, 4*x^3 - 3*x, 8*x^4 - 8*x^2 + 1]

    g=chebyshevU([1 ,2, 3 ,4],x) %second kind
    [ 2*x, 4*x^2 - 1, 8*x^3 - 4*x, 16*x^4 - 12*x^2 + 1]

    what coefficients should i take for this step?

    Thanks
     
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