File:Gauss-chebychev-integration.svg
Summary
| Description |
English: Example for Gauß-Chebychev-Integration/quadrature.
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| Date | |
| Source | Own work |
| Author | Accountalive |
| SVG development | Category:Valid SVG created with R code#Gauss-chebychev-integration.svg  Category:Translation possible - SVGThis file uses embedded text that can be easily translated using a text editor. |
| Source code | R codef <- function(x){ exp( x**3) }
n = 7
xi = cos(( 2*(n:1)-1 )/( 2*n ) * pi)
w = pi/n
width = w*sqrt(1-xi^2)
sum( width*f(xi)) #print approximated integral
# plot axis and labels
range = (-100:100)/100
maxx=sum(width)/2
plot(range,f(range),xlim=1.05*c(-1*maxx,maxx),ylim=c(0.01045,max(f(range))),
type="n",col=2,bty="l",
main = "Gauß-Tschebyschow-Integration\nn=7",
xlab = "x",
ylab = "y")
height = f(xi)
# recangles may start at < -1
curx=-sum(width)/2
# plot green boxes
for(i in 1:n)
{
y = c( 0, height[i], height[i], 0)
x = c( curx, curx, curx+width[i], curx+width[i])
polygon(x,y,density = -1,border=hsv(0.3,0.4,0.8),col=hsv(0.3,0.4,0.95))
curx=curx+width[i]
}
# plot (x_i, f(x_i))
lines(xi,height,type="p")
# plot f(x)
lines(range,f(range),type="l",col=2,lwd=1.5)
legend(-1, y = 2.5, c("f(x)","f(x_i)","Approximation"),bty="n",
col=c("red","black"),
pch=c(NA,1,NA),
lty=c(1,0,0),
fill=c(NA,NA,hsv(0.3,0.4,0.95)),
border=c(NA,NA,hsv(0.3,0.4,0.8)));
#abline(1,1) # to see whether plot has 1:1 aspect ratio)
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Licensing
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