# KEX-FrVFtlϕ

## Lԁia,bj̐ϕKEX-FrVFtϖ@ŌvZ܂B

 $\normal{\large\int_{\small a}^{\hspace{25}\small b}}f(x)dx={\large\int_{\small -1}^{\hspace{25}\small 1}}f({\large\frac{b-a}{2}}y+{\large\frac{b+a}{2}}){\large\frac{b-a}{2}}dy\\\hspace{70}\simeq {\large\frac{b-a}{2}\sum_{\small i=1}^{n}}w_{i}\sqrt{1-y_i^2}f(x_i)\\\hspace{10}x_i={\large\frac{b-a}{2}}y_i+{\large\frac{b+a}{2}},\hspace{10}y_i=cos{\large\frac{2i-1}{2n}}\pi,\hspace{10} w_i={\large\frac{\pi}{n}}\\$
 f(x) a , b 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
 61014182226303438424650
 ʓIɍxŋ܂܂Bϕ֐f(x)́A͓Ił邱ƂƎ֐łȂƂOƂĂ܂B$\normal Gauss-Chebyshev\ integration\\(1)\ {\large\int_{\small -1}^{\hspace{25}\small 1}}{\large \frac{f(x)}{\sqrt{1-x^2}}}dx\simeq {\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\hspace{30}nodes\hspace{35} x_i=-cos{\frac{2i-1}{2n}}\pi\\\hspace{30}weights\hspace{20} w_i={\large\frac{\pi}{n}}\\$

AP[gɂ͒L܂B
M܂B

y KEX-`FrVFtlϕ z̃AP[gL
j
N
20Ζ 20Α 30Α 40Α 50Α 60Έȏ
E
Ew ZEEwEw@ w ЈE c GWjA tE ̑
̌vZ
ɖɗ ɗ ɗ ɗȂ
gpړI
ӌEzioO񍐂) oOɊւ (AP[gj
vZoO(͒lƊԈĂ錋ʁAʁAQlȂ)
oO(ԈĂƐȂ)
AP[g͉Lɂql̐ƂČfڂĂƂ܂B