File:Chebyshev-nodes-by-projection.svg
Summary
| Description |
English: This is an illustration of Chebyshev nodes, which can be visualized as the x-coordinates of equally spaced points on a unit semicircle. |
| Date | |
| Source | Own work |
| Author | Steven G. Johnson |
Created in Julia using Matplotlib/PyPlot using the following code:
using PyPlot
n = 10
θₙ = π*(2(1:n) .- 1)/(2n)
θ = linspace(0,pi, 300)
plot(cos.(θ), sin.(θ), color="gray")
plot([-1.2,1.2], [0,0], color="gray")
plot(cos.(θₙ), sin.(θₙ), "bo")
plot(cos.(θₙ), zeros(θₙ), "ro")
text(0,-0.15, "Chebyshev nodes", horizontalalignment="center", color="red", fontsize=15)
for k = 1:n
x,y = cos(θₙ[k]), sin(θₙ[k])
arrow(x,y,0,-y+0.03, head_width=0.03, head_length=0.03, length_includes_head=true)
end
xticks(-1:0.2:1)
yticks(0:0.2:1)
axis("equal")
xlim(-1.2,1.2)
savefig("/Users/stevenj/Downloads/chebnodes.svg")
Licensing
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