Nodes and weights for the Gauss-Kronrod numerical integration method
Calculates the nodes and weights for the Gauss-Kronrod numerical integration.
| \(\normalsize Gauss-Kronrod\ quadrature\\ {\large\int_{\small -1}^{\small 1}}f(x)dx\simeq{\large\displaystyle \sum_{\small i=1}^{n}}w_{i}f(x_i)\\{\large\int_a^{b}}f(x)dx\simeq{\large\frac{b-a}{2}\displaystyle \sum_{\small i=1}^{n}}w_{i}f({\large\frac{b-a}{2}}x_i+{\large\frac{b+a}{2}})\\\) |
| \(\normalsize Gaussian\ quadrature\\ \hspace{20px} {\large\int_{\small a}^{\small b}}w(x)f(x)dx\simeq{\large\displaystyle \sum_{\small i=1}^{n}}w_{i}f(x_i)\\ Gauss-Kronrod\ quadrature\\ \hspace{30px} interval(a,b):\hspace{20px} [-1,\ 1]\\ \hspace{30px} w(x):\hspace{80px} 1\\ \hspace{30px} polynomialsl:\hspace{10px} P_n (x)\\ \) |
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