# Nodes and Weights of Gauss-Lobatto Calculator

## Calculates the nodes and weights of the Gauss-Lobatto quadrature.

 $\normal Gauss-Lobatto\ quadrature\\ {\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\frac{2}{n(n-1)}}(f(-1)+f(1))+{\large\sum_{\small i=2}^{n-1}}w_{i}f(x_i)\\\ nodes\hspace{30} x_i:\ the\ i-th\ zeros\ of\ P_{n-1}^'(x)\\\ weights\hspace{15} w_i={\large\frac{2}{n(n-1)[P_{n-1}(x_i)]^2}}\\$
 n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 n=2,3,4,..,100 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Gaussian\ quadrature\\\hspace{20} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\Gauss-Lobatto\ quadrature\\\hspace{30} interval(a,b):\hspace{20} [-1,\ 1]\\\hspace{30} w(x):\hspace{80} 1\\\hspace{30} polynomials:\hspace{10} P'_{n-1} (x)\\$
Nodes and Weights of Gauss-Lobatto
 [1-8] /8 Disp-Num5103050100200
[1]  2015/11/18 14:32   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
project work for my masters graduate
Comment/Request
My request is.... how can i get the x and y co-ordinates of a qudrilateral from these nodes and weights?? tat would be very helpful.
[2]  2014/08/05 02:28   Male / 20 years old level / An engineer / Very /
Purpose of use
Working on a financial derivative's risk neutral density with the double Heston LV model using Gauss-Lobatto Quadrature, needed to check some numbers; very helpful
[3]  2014/06/19 07:49   Male / 20 years old level / A teacher / A researcher / Very /
Purpose of use
Non-linear modeling
[4]  2014/04/07 13:34   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
for to do scripsion
Comment/Request
thanks so much
[5]  2014/02/14 05:47   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
searched for a table or formula, want to write code for adaptive generalized filon-quadrature
following Iserles Lobatto nodes perform best
[6]  2013/09/08 21:23   Female / 30 years old level / High-school/ University/ Grad student / A little /
[7]  2011/05/10 21:47   Male / 30 years old level / A teacher / A researcher / Very /
Purpose of use
To check if the points in my program are the same as here and to use the weights
[8]  2010/10/17 20:38   - / 50 level / A teacher / Very /
Purpose of use
research
Comment/Request
COULD YOU KINDLY SEND ME ALL GAUSSLOBATTO RULES UP TO HUNDRED.MANY THANKS

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