quadrature rule has the highest possible order











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Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$




Do I need to use the formula,
$$w_j = frac{2}{(1-x_j^2)
(P'_n(x_j))^2}$$



If so how do I use it? what is $x_j$ and $P'_n$?






numerical-methods







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    Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$




    Do I need to use the formula,
    $$w_j = frac{2}{(1-x_j^2)
    (P'_n(x_j))^2}$$



    If so how do I use it? what is $x_j$ and $P'_n$?






    numerical-methods







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite












      Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$




      Do I need to use the formula,
      $$w_j = frac{2}{(1-x_j^2)
      (P'_n(x_j))^2}$$



      If so how do I use it? what is $x_j$ and $P'_n$?






      numerical-methods







      share|cite|improve this question














      Find the weights $w_0, w_1$ and the abscissa $x_0$ such that the following quadrature rule has the highest possible order: $$int_0^1 f(x) dx approx w_0f(x_0) + w_1 f(1)$$




      Do I need to use the formula,
      $$w_j = frac{2}{(1-x_j^2)
      (P'_n(x_j))^2}$$



      If so how do I use it? what is $x_j$ and $P'_n$?






      numerical-methods




      numerical-methods






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      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked yesterday









      user123

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          The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.






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          • I havemade another post about this question with more detail, could you help?
            – user123
            11 hours ago











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          up vote
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          The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.






          share|cite|improve this answer























          • I havemade another post about this question with more detail, could you help?
            – user123
            11 hours ago















          up vote
          0
          down vote













          The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.






          share|cite|improve this answer























          • I havemade another post about this question with more detail, could you help?
            – user123
            11 hours ago













          up vote
          0
          down vote










          up vote
          0
          down vote









          The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.






          share|cite|improve this answer














          The abscissas $(x_j)$ are the zeros of the $n$th orthogonal polynomial; here $n=2$ and $P_2$ is the second Legendre polynomial (only the domain of definition has been altered from $[-1,1]$ to $[0,1]$ so you need to change variable. Read about Gaussian quadratures.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited yesterday

























          answered yesterday









          Richard Martin

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          • I havemade another post about this question with more detail, could you help?
            – user123
            11 hours ago


















          • I havemade another post about this question with more detail, could you help?
            – user123
            11 hours ago
















          I havemade another post about this question with more detail, could you help?
          – user123
          11 hours ago




          I havemade another post about this question with more detail, could you help?
          – user123
          11 hours ago


















           

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